For example, what was the narrative purpose of that moment where Kirk asks McCoy what Spock would do if Kirk was in Spock's position? McCoy said he'd leave Kirk to die as if to imply that Spock would under no circumstance violate any rule even if it meant saving the life of someone important. There is no moment in this film that pays off this exchange nor is there any moment where Spock himself violates any kind of rule to save Kirk in the end. It's a long drawn out moment that never pays off.
It does pay off all the way through the movie. It helps to define the differences in Kirk and Spock.
Another call back to it is Khan's "You can't break rules, how can you be expected to break bones" speech.
Kirk and Spock are both evolving--growing up. Kirk has to learn that you can't always take risks, you can't let your emotions control you, that rules exist for a reason, he needs to be more mature, more serious.
Spock has to learn that you can't stick strictly to the letter of the rules a 100% of the time. You've gotta take risks, sometimes act on your emotions. That sometimes doing moral things mean not following the rules.
You complain when they don't give women anything to do, you complain when they do. Just because Uhura was unsuccessful negotiating with Klingons doesn't mean she sucks at her job.
It reminds me of when Damon Lindelof said that they had talked about an early idea where Uhura has to negotiate with a Klingon fleet that's heading to Earth while Spock is fighting Khan. And some fans got very angry about how such an important job is given to Uhura. I'm sure many of them were the same ones who go on about how "She's just defined by her relationship with Spock."
That would have rocked. Put her in the center-seat, and just have her own the scene.