I changes the rear brake pads and rotors on my R53, which went smoothly, however, I broke one of the caliper spring clips off inside of the caliper. I guess it rusted itself into place. The hole goes all the way though the caliper, but there isn't much room to work with. Any ideas how to get the little metal stub out?

 

I'd try to punch it thru since the hole goes all the way

if that fails, drill it carefully ...

these are the methods I'd try

 

+1 for the hammer and punch approach.