Kirk's jump from cadet to captain has been discussed to death but I think it can be explained away the fact that he was being groomed for command (Kobyashi Meru) and that he had proven command ability (the Nero incident). It also fits with the prime universe statement that he was the youngest captain in the fleet.
What about everyone else?
Kirk, Uhura and McCoy were obviously still cadets at the time of Nero's attack. In the shuttle hanger at the academy, Spock referred to Uhura as "lieutenant" however on Enterprise Captain Pike addressed her as "cadet." McCoy (also a cadet) referred to him as one Captain Pike's "senior medical staff" and is wearing Lt. Commander's stripes. Letís assume Kirk was not grounded for cheating. What would his assignment have been? Where does this leave Sulu and Checkov? Are they also cadets and it was just not shown? Does Cadet/Lt. Uhura outrank Ensign Checkov. Was everyone just given a temporary field promotion due to the fact that these ships were heavily staffed by cadets?
The only one that seems to make any sense is Spock. If all cadets were wearing red uniforms then we can assume that Spock's grey uniform was indicative of him being a graduate and an officer. They grey uniform was presumably his ground uniform while the more familiar blue tunic shows his position as Pike's science officer.