Most of the time when I run a fullscreen game, my mouse shows up in the center of the screen at first(as would be expected). But the moment I move the mouse at all, it quickly flies off the right of the screen and never returns. I found that when this happens in a game, running the same game in windowed mode causes the mouse to act normal.
Also, there is another issue with my mouse that may or may not be related. It stops working, randomly as far as I can tell, sometimes. I have found that unplugging the mouse and plugging it back in makes it work normally again.
Also note that this doesn't occur in Windows, only Linux, so the mouse itself is not broken.
My mouse is a wireless USB mouse from Logitech.

I've had that problem with a mouse before. It would function correctly on a windows box but Debian, Fedora, and Slack did not like it. The curser would fly over to the right side of the screen and it would act weird. You might try to see if you can modify Xorg or Xfree to make it work correctly, but you may just need to try another mouse.

Thanks for the help, I'll see if I can find a standard ps2 mouse somewhere to try out.