[Drew]

Well, it's either your bushings are worn, or the arm holder itself is loose. Most likely it's the former - a bit of teflon tape around the inside, or popping off the bushigs and coating the inside with nail polish and then putting them back on is the way to go.

However, if you're actually hearing rattling, that almost makes me wonder if the arm holder is loose. Take off the back of the trem cover, and see if the bit that the bar pops into has any play in it. If so, a socket wrench and, probably, a flat head screwdriver on the front is the way to go, though be careful with that screwdriver so it doesn't slip and gouge up the guitar.