My favorite moments in the new movie when we were shown the competence of each character. All too often in other movies the characters were made to look incompetent for the sake of a plot point (e.g. McCoy didn't know enough about Klingon physiology to save a life in Undiscovered Country) or comedy (e.g. Uhura didn't know Klingon in UC, Scotty walks into a bulkhead after stating he knows every inch of the ship).
If the Enterprise is the best ship in the fleet, it's because of her crew. So it was very nice to see them shown as the best and brightest of Star Fleet.