You can pop the L1 and R1 buttons off without taking apart the controller. You'll see two posts on the controller that the buttons slide onto. Mine had a little bit of white powder on them. Wipe the posts down with a paper towel. Then, on the back of the buttons, you can spray compressed air into the holes which those posts go into or just put a little WD-40 in there. Pop them back on, and they should be fine. I haven't had a problem with mine since.
I had the same problem, and this fixed it right up. I concur, you do not need to open the controller to pop off the buttons, just be gentle and go slow from one edge toward center, once the button is shifted slightly off center, then move to the other side and it should pop off. There is a singe snap clip at the top center of the button that you need to dislodge, just go slow and be gentle (I used a wooden toothpick to avoid scratches). Thanks for risking your hardware for the rest of us, it really is appreciated.
As a footnote, I would strongly urge everyone to refrain from using WD40 on any plastic (it can damage/destroy certain polymers), in a pinch silicone spray might be used, but really anything you put in there will attract dust and may in time prove a bigger problem to clean out. I also would suggest to the mods to sticky this thread or just make it easier to find, like a DualShock 4 subsection. Just my 2¢. Cheers!
I will be one of the most polite adversaries you will ever meet. I will neither teabag nor taunt after a kill. Nevertheless, steal my weapon and I will hunt you down mercilessly without regard for team or personal score. Fair warning.