Continuity mistake: In the original UK VHS version of the movie, Scotty beams the Klingons aboard the Enterprise using the controls in the booth (located behind a glass screen). The shot cuts from the booth interior to the Enterprise senior officers awaiting the arrival of the Klingons on the transporter pad - Scotty is suddenly in front of the glass and in the line-up. The shot cuts back to the interior of the booth and Scotty is back in there, operating the controls.
Continuity mistake: When Kirk and Sulu are talking about the details of the peace conference, you can see Sulu on the small display behind Kirk. When Kirk asks when the conference starts, you can see on the small display that someone leans in to tell Sulu the information. When the camera cuts to Sulu the person is no longer leaning in but is standing behind Sulu. (01:28:20)
Revealing mistake: When the Enterprise begins to leave the spacedock, the background inside spacedock (behind Enterprise) seems to move in two different directions, the top moves towards the right, the bottom towards the left.
Continuity mistake: At the dinner you can see the contents in Kirk's glass changing from full, to nearly empty, to half-full again, without Kirk either drinking from the glass or having the glass refilled.
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.
Character mistake: There's no apparent reason for Spock's conviction that the gravity boots are a damning piece of evidence that will reveal the assassins, especially considering how useless they prove to be after being found planted in an innocent man's locker.
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.
Continuity mistake: When Valeris advises Kirk that there is a supply of Romulan ale onboard, the clock behind her reads 16:14:08. After Kirk commends her and leaves the bridge and the camera switches to Spock, the clock reads 16:14:06. (00:19:25)
Continuity mistake: After welcoming Gorkon to dinner, Kirk walks over to Spock and says "I hope you're happy". The clock behind Spock first shows 16:13:57 as Kirk is walking over, and then 16:13:55 when he reaches Spock. (00:19:20)
Continuity mistake: In the opening scene when Sulu is on the bridge and the energy wave begins vibrating the Excelsior, when Sulu's tea cup begins vibrating across the table, it's first seen closer to Sulu. The next close shot shows it vibrating right to the edge of the table. Yet in the next wide shot, it's back where it was near Sulu again. Then in the following close, it's back at the edge, this time sliding off to the floor. (00:04:00)
Continuity mistake: When the Excelsior enters the battle in orbit of Khitomer, General Chang's Bird Of Prey is on top of her. However, when he orders to fire upon her, she is hit from below.
Continuity mistake: At the end, as the crew are talking about being arrested for feelings, the time on the bridge clock is 17:56:19 as Chekov sits down. We hear the viewscreen activate, cut to see Sulu talking, and the time above the screen is suddenly 17:56:28.
Continuity mistake: Valeris seems to appear out of nowhere during the thwarted assassination attempt on Khitomer. The Enterprise crew beam down without her, spring into action, and when Admiral Cartwright yells "Arrest those men!" Spock emerges from the crowd with Valeris in his custody as if she were always there with him or he'd pulled her out of a hat.
Character mistake: Chekov pulls a gun on the Klingon ambassador even though he hasn't been implicated in the conspiracy.