After my games I nearly always analyze them with a computer engine to see where mistakes were made. Normally I do not pay much attention to the engine analysis for my opponent's moves, for the reason that I can only remember so many lessons per game. So I'm wondering, those of you who engine analyze games afterwards, do you spend time inspecting the errors your opponents make as well?

I use Fritz8 Blunder Check. With that you can select which color's moves are to be checked, with one choice being BOTH. I generally select BOTH. I want to know if my opponent missed something good. Fritz8 runs pretty fast, so it doesn't take all that long to look at both sides.

Yes.  Quite simply I analyse every move of every game I play. 

Sometimes I find really good moves my opponent missed which highlight why my previous move might be wrong. 

I also analyse variation lines on "best" moves missed and try to find out why a move I made was not so great and why the "best move" is better.