Q:

Why is the DataGridRow IsSelected binding not working on DataGrid

In Josh Smith's MVVM demo he's uses a ListView with a ListViewItem style like this:
<Style x:Key="CustomerItemStyle" TargetType="{x:Type ListViewItem}">
    <Setter Property="IsSelected" Value="{Binding Path=IsSelected, Mode=TwoWay}" />
    <Style.Triggers>
        <MultiTrigger>
            <MultiTrigger.Conditions>
                <Condition Property="ItemsControl.AlternationIndex" Value="1" />
                <Condition Property="IsSelected" Value="False" />
                <Condition Property="IsMouseOver" Value="False" />
            </MultiTrigger.Conditions>
            <Setter Property="Background" Value="#EEEEEEEE" />
        </MultiTrigger>
    </Style.Triggers>
</Style>

It binds the IsSelected property nicely. The style is applied to the ListView like so:
<ListView  
  ItemContainerStyle="{StaticResource CustomerItemStyle}"
  ItemsSource="{Binding}"
  >

My Version
I have tried binding IsSelected in a similar way with a DataGrid through DataGridRow. However it is causing issues when items are selected through the collection of item ViewModels, where the IsSelected property is defined. 
As it is using a two way binding I would have thought that items could be selected through the UI and the collection of item ViewModels.
Let's say I select items through the UI, this works fine. I can select a singular item and then use [shift] to select a range, then using [ctrl] select some more items. Deselecting items works correctly as well.
However I select a bunch via the collection. Let's say upon the click of a button (as I do in the code below), a bunch of items get selected. When I scroll down the DataGrid then some are selected as they should be some are not. If I select one item through the UI then only some of the items are deselected and some remain selected, it's all a bit funky. Even the Select All button in the top left doesn't perform quite right.
Code
All code is below, at the bottom is the view the key piece there is the DataGridRow style with IsSelected binding.
Here is my user class:
using System.ComponentModel;

namespace WpfAppDataGrid.Model
{
    public class User : INotifyPropertyChanged
    {
        public static User CreateNewUser()
        {
            return new User();
        }

        public User() { }

        public int User_ID { get; set; }
        public string Username { get; set; }
        public string Name { get; set; }
        public string Job_Title { get; set; }
        public string Department { get; set; }
        public string Company { get; set; }
        public string Phone_Office { get; set; }
        public string Phone_Mobile { get; set; }
        public string Email { get; set; }

        public event PropertyChangedEventHandler PropertyChanged;

        private void RaisePropertyChanged(string propertyName)
        {
            if (PropertyChanged != null)
                PropertyChanged(this, new System.ComponentModel.PropertyChangedEventArgs(propertyName));

        }
    }
}

Here is the UserViewModel, where IsSelected resides:
using System;
using System.ComponentModel;
using WpfAppDataGrid.DataAccess;
using WpfAppDataGrid.Model;

namespace WpfAppDataGrid.ViewModel
{
    class UserViewModel : INotifyPropertyChanged
    {
        readonly User _user;
        readonly UserRepository _userRepository;
        bool _isSelected;

        public UserViewModel(User user, UserRepository userRepository)
        {
            if (user == null)
                throw new ArgumentNullException("user");

            if (userRepository == null)
                throw new ArgumentNullException("userRepository");

            _user = user;
            _userRepository = userRepository;
        }
        public UserViewModel()
        {
        }

        public int User_ID
        {
            get { return _user.User_ID; }
            set
            {
                if (value == _user.User_ID)
                    return;

                _user.User_ID = value;

                RaisePropertyChanged("User_ID");
            }
        }

        public string Username
        {
            get { return _user.Username; }
            set
            {
                if (value == _user.Username)
                    return;

                _user.Username = value;

                RaisePropertyChanged("Username");
            }
        }
        public string Name
        {
            get { return _user.Name; }
            set
            {
                if (value == _user.Name)
                    return;

                _user.Name = value;

                RaisePropertyChanged("Name");
            }
        }
        public string Job_Title
        {
            get { return _user.Job_Title; }
            set
            {
                if (value == _user.Job_Title)
                    return;

                _user.Job_Title = value;

                RaisePropertyChanged("Job_Title");
            }
        }
        public string Department
        {
            get { return _user.Department; }
            set
            {
                if (value == _user.Department)
                    return;

                _user.Department = value;

                RaisePropertyChanged("Department");
            }
        }
        public string Company
        {
            get { return _user.Company; }
            set
            {
                if (value == _user.Company)
                    return;

                _user.Company = value;

                RaisePropertyChanged("Company");
            }
        }
        public string Phone_Office
        {
            get { return _user.Phone_Office; }
            set
            {
                if (value == _user.Phone_Office)
                    return;

                _user.Phone_Office = value;

                RaisePropertyChanged("Phone_Office");
            }
        }
        public string Phone_Mobile
        {
            get { return _user.Phone_Mobile; }
            set
            {
                if (value == _user.Phone_Mobile)
                    return;

                _user.Phone_Mobile = value;

                RaisePropertyChanged("Phone_Mobile");
            }
        }
        public string Email
        {
            get { return _user.Email; }
            set
            {
                if (value == _user.Email)
                    return;

                _user.Email = value;

                RaisePropertyChanged("Email");
            }
        }

        /// <summary>
        /// Gets/sets whether this customer is selected in the UI.
        /// </summary>
        public bool IsSelected
        {
            get { return _isSelected; }
            set
            {
                if (value == _isSelected)
                    return;

                _isSelected = value;

                RaisePropertyChanged("IsSelected");
            }
        }

        public event PropertyChangedEventHandler PropertyChanged;

        private void RaisePropertyChanged(string propertyName)
        {
            if (PropertyChanged != null)
                PropertyChanged(this, new System.ComponentModel.PropertyChangedEventArgs(propertyName));

        }
    }
}

Here is my AllUsersViewModel:
using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Collections.Specialized;
using System.ComponentModel;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Data;
using System.Windows.Input;
using WpfAppDataGrid.DataAccess;

namespace WpfAppDataGrid.ViewModel
{
    class AllUsersViewModel : INotifyPropertyChanged
    {
        readonly UserRepository _userRepository;

        public AllUsersViewModel()
        {
            _userRepository = new UserRepository();
            _userRepository.LoadUsers();
            CreateAllUsers();
        }

        void CreateAllUsers()
        {
            List<UserViewModel> all =
                (from usr in _userRepository.GetUsers()
                 select new UserViewModel(usr, _userRepository)).ToList();

            foreach (UserViewModel uvm in all)
            {
                uvm.PropertyChanged += this.OnUserViewModelPropertyChanged;
            }
            this.UserCollection = new ObservableCollection<UserViewModel>(all);
            this.UserCollection.CollectionChanged += this.OnCollectionChanged;
        }

        private ObservableCollection<UserViewModel> userCollection;
        public ObservableCollection<UserViewModel> UserCollection
        {
            get
            {
                return userCollection;
            }
            set
            {
                userCollection = value;
                RaisePropertyChanged("UserCollection");
            }
        }

        RelayCommand selectItemsCommand;

        public ICommand SelectItemsCommand
        {
            get
            {
                if (selectItemsCommand == null)
                    selectItemsCommand = new RelayCommand(SelectItemsCommandExecute, CanSelectItemsCommand);
                return selectItemsCommand;
            }
        }

        private void SelectItemsCommandExecute(object parameter)
        {
            for (int i = 4; i <= 49; i++)
            {
                UserCollection[i].IsSelected = true;
            }
        }

        private bool CanSelectItemsCommand(object parameter)
        {
            return true;
        }

        void OnCollectionChanged(object sender, NotifyCollectionChangedEventArgs e)
        {
            if (e.NewItems != null && e.NewItems.Count != 0)
                foreach (UserViewModel userVM in e.NewItems)
                    userVM.PropertyChanged += this.OnUserViewModelPropertyChanged;

            if (e.OldItems != null && e.OldItems.Count != 0)
                foreach (UserViewModel userVM in e.OldItems)
                    userVM.PropertyChanged -= this.OnUserViewModelPropertyChanged;

        }

        void OnUserViewModelPropertyChanged(object sender, PropertyChangedEventArgs e)
        {
            string IsSelected = "IsSelected";

            if (e.PropertyName == IsSelected)
                this.RaisePropertyChanged("TotalSelectedUsers");
        }

        public event PropertyChangedEventHandler PropertyChanged;
        private void RaisePropertyChanged(string propertyName)
        {
            if (PropertyChanged != null)
            {
                PropertyChanged(this, new System.ComponentModel.PropertyChangedEventArgs(propertyName));
            }
        }
    }

    public class RelayCommand : ICommand
    {
        readonly Action<object> _execute;
        readonly Predicate<object> _canExecute;

        /// <summary>
        /// Creates a new command that can always execute.
        /// </summary>
        /// <param name="execute">The execution logic.</param>
        public RelayCommand(Action<object> execute)
            : this(execute, null)
        {
        }

        /// <summary>
        /// Creates a new command.
        /// </summary>
        /// <param name="execute">The execution logic.</param>
        /// <param name="canExecute">The execution status logic.</param>
        public RelayCommand(Action<object> execute, Predicate<object> canExecute)
        {
            if (execute == null)
                throw new ArgumentNullException("execute");

            _execute = execute;
            _canExecute = canExecute;
        }

        [DebuggerStepThrough]
        public bool CanExecute(object parameter)
        {
            return _canExecute == null ? true : _canExecute(parameter);
        }

        public event EventHandler CanExecuteChanged
        {
            add { CommandManager.RequerySuggested += value; }
            remove { CommandManager.RequerySuggested -= value; }
        }

        public void Execute(object parameter)
        {
            _execute(parameter);
        }
    }
}

Here is the user repository where I create the users:
using System.Collections.ObjectModel;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using WpfAppDataGrid.Model;

namespace WpfAppDataGrid.DataAccess
{
    public class UserRepository
    {
        ObservableCollection<User> _users = new ObservableCollection<User>();

        public UserRepository()
        {
        }

        public ObservableCollection<User> GetUsers()
        {
            return _users;
        }

        public void LoadUsers()
        {
            int i = 0;
            while (i < 1000)
            {
                i++;
                var user = new User();
                user.User_ID = i;
                user.Username = RandomString(8, true);
                user.Name = user.Username + " " + RandomString(8, true);
                user.Job_Title = RandomString(8, true);
                user.Department = RandomString(8, true);
                user.Company = RandomString(10, true);
                user.Phone_Office = "07 " + RandomNumber(5200, 6700) + " " + RandomNumber(1000, 9999);
                user.Phone_Mobile = "04 " + RandomNumber(2800, 4500) + " " + RandomNumber(1000, 9999);
                user.Email = user.Username + "@gmail.com";
                _users.Add(user);
            }
        }

        private static Random randomSeed = new Random();
        public static string RandomString(int size, bool lowerCase)
        {
            StringBuilder RandStr = new StringBuilder(size);
            int Start = (lowerCase) ? 97 : 65;

            for (int i = 0; i < size; i++)
                RandStr.Append((char)(26 * randomSeed.NextDouble() + Start));

            return RandStr.ToString();
        }

        private int RandomNumber(int min, int max)
        {
            return randomSeed.Next(min, max);
        }
    }
}

And finally here is the view for all users:
<Window x:Class="WpfAppDataGrid.View.AllUsersView"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:viewmodel="clr-namespace:WpfAppDataGrid.ViewModel"
        Title="AllUsersView" Height="450" Width="820">

    <Window.DataContext>
        <viewmodel:AllUsersViewModel />
    </Window.DataContext>

    <Window.Resources>
        <Style x:Key="UserRowStyle" TargetType="{x:Type DataGridRow}">
            <Setter Property="IsSelected" Value="{Binding Path=IsSelected, Mode=TwoWay}" />
            <Setter Property="BorderBrush" Value="DarkGray" />
            <Setter Property="BorderThickness" Value="0,0,1,0"/>
            <Setter Property="Background" Value="Transparent"/>
            <Setter Property="Foreground" Value="Black"/>
            <Setter Property="Template">
                <Setter.Value>
                    <ControlTemplate TargetType="{x:Type DataGridRow}">
                        <Grid>
                            <Border x:Name="DGR_BackingBorder" BorderBrush="Orange" BorderThickness="1,2,1,2" Background="Transparent">
                            </Border>
                            <Border x:Name="DGR_Border" 
                                    BorderBrush="{TemplateBinding BorderBrush}" 
                                    BorderThickness="1,2,1,2" 
                                    Background="{TemplateBinding Background}"
                                    SnapsToDevicePixels="True">

                                <SelectiveScrollingGrid>
                                    <SelectiveScrollingGrid.ColumnDefinitions>
                                        <ColumnDefinition Width="Auto" />
                                        <ColumnDefinition Width="*" />
                                    </SelectiveScrollingGrid.ColumnDefinitions>
                                    <SelectiveScrollingGrid.RowDefinitions>
                                        <RowDefinition Height="*" />
                                        <RowDefinition Height="Auto" />
                                    </SelectiveScrollingGrid.RowDefinitions>
                                    <DataGridCellsPresenter x:Name="DGR_CellsPresenter" Grid.Column="1" ItemsPanel="{TemplateBinding ItemsPanel}" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" />
                                    <DataGridDetailsPresenter x:Name="DGR_DetailsPresenter" Grid.Column="1" Grid.Row="1"
                                                          SelectiveScrollingGrid.SelectiveScrollingOrientation="{Binding AreRowDetailsFrozen, ConverterParameter={x:Static SelectiveScrollingOrientation.Vertical}, Converter={x:Static DataGrid.RowDetailsScrollingConverter}, RelativeSource={RelativeSource AncestorType={x:Type DataGrid}}}"
                                                          Visibility="{TemplateBinding DetailsVisibility}" />
                                    <DataGridRowHeader Foreground="White" Grid.RowSpan="2" SelectiveScrollingGrid.SelectiveScrollingOrientation="Vertical"
                                                   Visibility="{Binding HeadersVisibility, ConverterParameter={x:Static DataGridHeadersVisibility.Row}, Converter={x:Static DataGrid.HeadersVisibilityConverter}, RelativeSource={RelativeSource AncestorType={x:Type DataGrid}}}" />
                                </SelectiveScrollingGrid>
                            </Border>
                        </Grid>
                        <ControlTemplate.Triggers>
                            <Trigger Property="IsMouseOver" Value="True">
                                <Setter TargetName="DGR_Border" Property="BorderBrush" Value="Transparent" />
                                <Setter TargetName="DGR_Border" Property="BorderThickness" Value="1,2,1,2" />
                            </Trigger>
                            <Trigger Property="IsSelected" Value="True">
                                <Setter TargetName="DGR_Border" Property="BorderBrush" Value="DarkOrange"/>
                                <Setter TargetName="DGR_Border" Property="Background" Value="Orange"/>
                            </Trigger>
                        </ControlTemplate.Triggers>
                    </ControlTemplate>
                </Setter.Value>
            </Setter>
        </Style>

        <Style TargetType="{x:Type DataGridCell}" >
            <Setter Property="Background" Value="Transparent"/>
            <Setter Property="BorderBrush" Value="Transparent"/>
            <Setter Property="BorderThickness" Value="0" />
            <Setter Property="Foreground" Value="Black" />
        </Style>
    </Window.Resources>

    <Grid Name="gridUsers" Background="Transparent">

        <DockPanel Background="Transparent" Margin="2,10,2,2" >
            <Grid DockPanel.Dock="Bottom" Margin="0,2,4,2">
                <StackPanel HorizontalAlignment="Right" Orientation="Horizontal" VerticalAlignment="Center">
                    <Button Content="Select rows 5 to 50" Command="{Binding SelectItemsCommand}"/>
                    <TextBlock Text=" Total: " />
                    <ContentPresenter Content="{Binding  ElementName=GenericDataGrid, Path=ItemsSource.Count}" ContentStringFormat="0" />
                </StackPanel>
            </Grid>
            <DataGrid Name="GenericDataGrid" Background="Transparent"  
                      RowStyle="{StaticResource UserRowStyle}"
                      BorderThickness="0" 
                      CanUserReorderColumns="True" 
                      AutoGenerateColumns="False" 
                      ItemsSource="{Binding UserCollection}" 
                      HorizontalScrollBarVisibility="Auto" VerticalScrollBarVisibility="Auto"
                      CanUserAddRows="False">
                <DataGrid.Columns>
                    <DataGridTextColumn Header="ID" CanUserReorder="True" IsReadOnly="True" Binding="{Binding Path=User_ID,NotifyOnTargetUpdated=True}" />
                    <DataGridTextColumn Header="Name" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Name}"/>
                    <DataGridTextColumn Header="Username" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Username}"/>
                    <DataGridTextColumn Header="Job Title" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Job_Title}"/>
                    <DataGridTextColumn Header="Department" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Department}"/>
                    <DataGridTextColumn Header="Company" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Company}"/>
                    <DataGridTextColumn Header="Phone" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Phone_Office}"/>
                    <DataGridTextColumn Header="Mobile" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Phone_Mobile}"/>
                    <DataGridTextColumn Header="eMail" CanUserReorder="True" CanUserSort="True" Binding="{Binding Path=Email}"/>
                </DataGrid.Columns>
            </DataGrid>
        </DockPanel>
    </Grid>
</Window>

A:

Hank
Disabling virtualization, will definitely fix your problem at a performance cost.
you could disable recycling of the VirtualizingStackPanel as @nit suggested, but that will not resolve the issue fully.
A different approach is to use Attached behaviours.
there is a tested working solution by @Samuel Jack (used it before), it is for listbox  and MVVM and it works great.
selected items are bindable in two way mode.
http://blog.functionalfun.net/2009/02/how-to-databind-to-selecteditems.html
As it's for ListBox, I uploaded a modified solution for DataGrid, It is a basic DataGrid with the desired functionality. 
https://www.sugarsync.com/pf/D6837746_80955217_331798
Enjoy

