Q:

Can blind people use web pages that utilize MOUSE events for interactions

Specific question is if I use something like:
$("#mytable").on("mousedown", "input", function(event) {...});

Is this accessibility 'friendly' or does this hinder a visually impaired person's ability to use my page?
Generically, are there other items I should stay away from in javascript & jquery?

A:

There is a simple way to test for the basic accessibility of this sort of interaction: Can you tab to the item and activate it using space or enter?
Accessibility is about more than blind people, there are other groups who rely on the keyboard as well but do not use a screen reader (e.g. people with mobility impairments). In either case it looks like there might be two issues:

A table is not typically an element you can focus on with the keyboard, so if the user gets information or activates functionality by clicking it, it should be selectable with the keyboard as well.
The 'mousedown' function is rarely accessible to keyboard users. (Although people using screen readers can probably use it by simulating a mouse click.)

Assuming the element is not a link or form control, you need to add tabindex (in the HTML or via JavaScript):
<table tabindex="0">

The 0 value puts it in the tabindex at the point it is in the DOM. (http://www.w3.org/TR/wai-aria-practices/#focus_tabindex)
Then you should ensure that a keypress also triggers the event, something like this should do it:
$("#test").mousedown(function() {
    // your function
});

// also activate with enter/space
$("#test").on("keydown", 
   function (e) {
    if (e.which === 13 || e.which === 32) {
        $('#test').click();
    } 
  }
);

(JavaScript/jQuery isn't my strongest point, please check the keycodes and improve as you see fit. It should enable people to press space or enter to activate the control.)
Generally, I would look for a JavaScipt library that has considered accessibility and talks about using WAI-ARIA. JQuery and jQuery UI are one of the better ones, but it is useful to test things as well. Using standard HTML controls and enhancing with JS is generally the safest approach, it's probably best to create a basic test and ask questions on a list like WebAim. 

