Other mistake: Every time we see a high ranking Starfleet Officer in the Starfleet Command scenes, they are wearing dozens of different badges and medals. Why don't Kirk and crew have any? In just the movies, Kirk and Co. have saved Earth twice and foiled an internal assassination attempt against the Federation President, as well as all the heroic and successful missions carried out in the original series. In the classic episode "Court-Martial" it lists Kirk as receiving the Starfleet Medal of Honor, the Silver Palm with Cluster, Starfleet Citation of Conspicuous Gallantry and Kragite Order of Heroism. And it is appropriate to Starfleet regulations to wear them. Kirk was wearing two decorations in the TOS episode "Court Martial" when he was framed for a crewmans' death.
Add timeGrumpy Scot
Other mistake: When Sulu tells Kirk he is coming to help, he states the Excelsior is currently in the Alpha Quadrant. The problem is the the Alpha Quadrant in the Star Trek universe is one quarter of the total Milky Way Galaxy. While technically correct, Sulu giving his position as in the Alpha Quadrant is useless to Kirk in terms of knowing when to expect help. It doesn't matter where Khitomer is in the galaxy. Sulu saying he is in the Alpha Quadrant gives Kirk absolutely no idea of when he will arrive. He could be anywhere from 5 minutes away to 5 weeks away or even further. Remember, it was originally projected to take Voyager 70 years to go from the Delta Quadrant back to the Federation in the Alpha Quadrant.