I don't know about all the plot points or character decisions, but last time I watched it, there was one thing that really stood out much more ridiculous than anything else. The idea that the crew refused to get to escape pods as the ship was going down... over Earth! I mean, who did they think they were saving? Everyone could have gotten out safely (as far as they knew) and just lost a ship. I mean, it's not like the Enterprise in the JJ films feels anything like it's a character of the show like it had in previous incarnations.
I could go on for days about all the stuff that makes no sense. In fact I disliked the movie so much upon first viewing, I felt I had to vent my spleen about it, and I wrote out all my complaints in a Word doc that was 10 pages long. It's an exasperating movie logic/plot-wise.