In this Universe, the senior staff of Kirk's Enterprise seems to be run more like what we see on the Serenity in "Firefly" rather than on the Starfleet vessels we are used to seeing in other Trek incarnations. If the ship's captain is dying in the aftermath of a battle, maybe the Chief Medical Officer should be there, not the head communications officer who should be getting communications back up and running. I also suspect that Sulu would be a better fighter to beam down to save Spock and apprehend Khan... BUT Uhura IS
Spock's girlfriend, after all....!
I am not so happy with the familiarity that goes on between Uhura and Kirk and not so approving of her moody 'tude in her job (can not imagine Shatner's Kirk or Picard or Sisko or Janeway or Archer tolerating this sort of behavior from a subordinate). I don't care for it, but this film has more of an action/buddy film feel/tone to it and -like Transformers needed a Mikaela Banes, TPTB decided nuTrek needed a hot & feisty, kick-ass female.
I actually do like how Uhura is given a more integral role in the action in the new Trek movies, and I see how Zoe Saldana's character adds an appealing dimension for both the 'boys and girls' in the audience (I know the usually-non-scifi-appreciating women I saw this movie with REALLY enjoyed her quips and actions), but -for me- her 'bad teenage girl' attitude and behavior goes a little bit too far at times.
Uhura probably needed to stay at her station when Spock went to engineering. Well... maybe not. And maybe McCoy needed to focus on the living in Sick Bay at that point. But we are needing to integrate this relationship into the important scenes of this movie. And this isn't "Tora! Tora! Tora!", after all, right? BUT-- Sulu, the trained fighter, needed to be sent down to immobilize Khan, not Uhura.