My biggest is when I remember that the character I'm playing is basically just an action figure. It's especially bad replaying a level in ME2 and realizing "well, fuck, no matter what option I pick, I always go down the exact same corridor fight the exact same bad guys, and do the exact same thing".
The other thing is when the game doesn't really stop me from massively changing my character's personality at the drop of a hat. I can turn him completely schizophrenic, and go from "loving earth-father" to "smarmy bastard" within the same dialogue, and the game doesn't bat an eye. It just makes the whole thing mechanical for me, which breaks any sense of caring I had about any of the characters.