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)
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: 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.
Deliberate mistake: It's not particularly believable that the away team to stop the assassination would consist of the ship's entire senior staff, and raises the question of who was left in charge of the bridge (the answer: apparently nobody, as they return to a completely deserted bridge). Of course this is dramatic license, and at this point the audience won't care or likely even notice.
Other mistake: Throughout the film, Valeris is referred to as a Starfleet Lieutenant. However, in every scene, she wears the rank of Commander on her uniform. Best comparison can be made in Star Trek II: The Wrath of Khan where the same uniforms were used. Saavik (Kirstie Alley) wore a Lieutenant rank (2 piece), where Chekov and Scotty (himself then still a Commander, until promoted by Admiral Morrow in Star Trek III) wore the single-piece rank insignia used by Valeris in The Undiscovered Country.
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: 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.