How unusual is getting a Masters degree in a slightly different field than Bachelors? Would it be out of the ordinary to get a Bachelors in Mechanical Engineering and then go for a Masters in something like Civil or Structural Engineering?

I don't know a lot about how transitioning to a Masters program works.. Do people usually continue on in the same field, or is branching out common?
This depends on where you are. In the US, this would generally not be too difficult, particularly if one uses elective courses at the bachelor's level to take some of the courses in the "new" field. 

Here in Germany, it would actually be almost impossible to switch as you've suggested. The reason for this is that the "prerequisite" for enrolling as master's student in a particular field is usually taken to be the bachelor's degree in the same field as taught at the university!  This is known as a "consecutive" degree requirement, and makes life very difficult for people coming from outside Germany.