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.
Suggested correction: The implication is that Excelsior has only very recently crossed the border from the Beta Quadrant to the Alpha Quadrant.
Other mistake: It was shown that whatever form Martia was in, whether it be the attractive semi-human form, the Sasquatch form, or the little girl form, her voice always remained the same. Why didn't her voice remain when she morphed into Kirk?
Suggested correction: Clearly she has the ability to control when and how her voice changes in the same way she controls her physical form.
Audio problem: When Spock mind melds with Valeris, you hear a heartbeat. Whose heartbeat is this? It is specifically stated in the original series that Vulcan hearts beat almost twice as fast as humans. It is, however, never established that Vulcan metabolic functions slow during a mind meld, due to conscious physical control or otherwise.
Suggested correction: The heartbeat is almost certainly not diegetic.
Suggested correction: It was "never established that Vulcan metabolic functions slow during a mind meld." Not "it was established that they do not." If something is not established one way or the other, then there is no contradiction and therefore no error.
Character mistake: At the trial, the witness said that "With the first shot, we lost our gravitational field. I found myself weightless, and unable to function." However, the first shot caused the ship to start listing to port. It was the second shot that caused the gravitational failure.
Suggested correction: People misremember events all the time, especially if the events are unexpected and chaotic. At best a character mistake.
I called it a character mistake.
He could also simply be lying in order to explain why he did not do whatever he should have after the 1st shot, since he was an easy target for the intruders and did not die in battle, which would have been honorable. Klingons are not the most honest of people.