Chosen Solution
My roommate and I have noticed that our PS3 controllers are beginning to press random buttons while in game, even when we are not holding them. All 3 of our controllers are doing the same things, particularly the square button and D pad are pushed. We have narrowed the problem down to happening most commonly when A) we hold the controller too tightly and B) we press the L2 bumper. Is there anything we can do here to fix these things instead of buying new ones?
You could take them apart and clean the controllers and you may have bumped the motherboard out of place making it sometimes hit random buttons. If after cleaning and making sure everything is put back properly and it still does it you may have to get new ones or go buy used controllers at a store or online.
Buy a new controller