I think the moment that cracks me up the most is the Red Shirt's excitement about "kicking some Romulan arse" or whatever, followed by a blank stare on the part of Sulu and Kirk.
It's the kind of thing that's satisfying as a long time fan because really the longer you've been following Trek the funnier that moment is.
There were a few clunky lines in the movie, and a few gratuitous bits that felt awkward, but whatever, mostly the humor worked.
Taking a step back for a moment I will say this: it is hard to give the destruction of a planet and the death of a few billion souls the weight it deserves when you are concerned with getting back to the funny action romp a few frames later.
Imagine the opening sequence of the film with a few wisecracks thrown in.