If you're talking about moments that just seemed flat-out weird, I nominate the parts in ME3 when you've used up the autodialogue with a crewmate, click on them again, and they say something like "Hey" or "Hello Shepard" as if they had forgotten that they'd just been having a conversation. (Yes, hello Liara - normally people say that at the start of a conversation rather than the end.)
The biggest "What?! I don't want to do that!" awkward moments were probably "machines can be broken" (some of my Shepards simply would not say that under any circumstances) and opening all the doors at once on the Purgatory prison ship. (Great idea, Shepard - open all the doors at once on a ship full of vicious criminals and corrupt guards. No way anything could *possibly* go wrong with that.) I often just spacebar both of those bits so I can imagine that something else happened instead.
Well, and not being able to challenge the Catalyst's premises.