Like people said just open it up and push everything back in place and clean it out a bit. I had the same R2 and L2 problem, just adjust the springs until it's springy again. Now my controller works like day 1 and I don't have the random button pushing problem anymore.
i once dropped my controller 3 times and after i picked it up after dropping it 3 times and every thing was fine.
i think the reasion your controller went out of controll after you droped it because it might be because you dropped it on carpit
Why hasen't sony qued in on this issue? I have same problem, I really don't wish to buy new controller, this ones barely a year old really. but I noticed I let it die, then it worked fine, well it charges and same problem, left analog stick goes to right and won't go left, I hit reset it works a little I start game, it **bleep** up, funny thing this all started when I got kicked from Defiance Games servers, and tried to get back in mulptle times, then controller like all **bleep** up, starts doing this junk, I contact them for help, they took like a week to get back post me some links about dis-connections, I said no, you broke my contoller you bleeps, you owe me a new one or 54 dollars for a new one 60 knowing ontario taxes,.but yeah Sony not queing in on this, cause they don`t give a **bleep**