I removed the passenger side vanity mirror light because it would not turn off. In the process it must have shorted something because the radio door locks, trunk radio and side mirrors are all non operational.

 

Those items are usually controlled by a body control module that has a fuse to protect it If you look in the maintenance and specifications section of your owners manual there are diagrams and explanations of which fuse protects what and its location.Check that fuse and if necessary replace it with the same size fuse.
Let us know how you make out with this , thanks.

 

Just curious, does the door locks work after the engine is started?

That fuse (inside fuse box) is usually located inside the cabin
Sometimes in a kick panel, sometimes under the dash, and again sometimes on the side
Maybe even be behind the coin holder