PS4 controller spins on certain games on the PS3. Is this a software problem?

I have a little problem with my PS4 controller and PS3.

With some games (e.g. Oblivion, Spider-Man: Web of Shadows) the L2 and R2 do not work at all. Oddly enough, the buttons work completely smoothly in the other games (e.g. Skyrim, GTA V, Black Ops 2, Uncharted).

Could this be a bug in the PS3 or PS4 controller software? Possibly an error in the compatibility between the console and the controller?

I myself suspect a compatibility error between PS3 and PS4 controller.

A good troubleshooting would be to knock the controller on the ground again and again until it leaves. Alternatively, you could always hit the PS3 on the floor.