When the shock wave from the Praxis explosion is first detected by one of the Excelsior's Bridge Officers, he informs Captain Sulu that the wave is approaching on the port side. At this point we see an exterior view of the Excelsior as the shock wave hits the ship from the starboard side.
The name of the character "Uhura" is misspelled "Uhuru" in the end credits. Uhuru is the Swahili word for freedom, and Uhura is the "girly" variant created by Gene Roddenberry for the original Star Trek (1966).
Although it makes a neat visual effect, and there were artistic and literary reasons for it (see trivia), the idea that Klingons have purple-pink blood is technically an inaccuracy within the Trek Universe. All other Trek movies and shows have consistently made clear that Klingons have red blood just like humans.
When Kirk reacts to the second torpedo fired at Kronos I his insignia pin is on the wrong side of his chest, revealing that the shot had been flipped.
When the Excelsior encounters the shock wave, Lieutenant Valtane starts next to Captain Sulu, then is shown near a console, then is shown moving *to* the console he was previously at. In this same edit, the Excelsior's humanoid alien crew member switches positions between shots, moving from the right to the left and then back to the right of the other Excelsior crew members.
Right at the moment Kronos One loses gravity, objects start to leap upward, including a Klingon officer's disruptor pistol. According to Newton's law of gravity, an object at rest stays at rest. No force is seen to cause that.
Right after the first torpedo hits the Klingon ship we see Klingons sitting at a table. Above them a large hanging light is swinging but on the table we see a tall mug sliding across the table. In a spaceship with artificial gravity emanating from the floor, the angle of pull would not change if the entire ship were to move. The downward force of the artificial gravity will most with everything else attached to the floor and therefore the items on the table would not have a 'low side' of the table to slide to. This was done perhaps to give the movie more of a sea battle feel like in the original series.
As the assassin at the Khitomer conference is preparing to fire, he pushes the muzzle of his rifle through a small circular hole cut in a frosted glass window. As the camera pans to show the assassin it is clear that the telescopic sight is mounted too high for him to be able to see his target.
Somehow, assassins from Enterprise can beam aboard the Chancellor's ship without alerting security but cannot use the transporter to dispose of their incriminating uniforms. However, 'alerting security' is not the reason given. Spock says that they could not beam them off the ship "for everyone to see".
It is never explained why the Romulans are participating in the peace conference. A Klingon-Federation alliance would be counter to Romulan interests. However, he could have been present represent the interests of the Romulan Empire which was the third major power in Star Trek at the time.
When the Enterprise rendezvouses with the Kronos One, Captain Kirk comments that he's never been this close to a Klingon ship. He has apparently forgotten that he flew a Klingon ship from the Genesis planet to Vulcan, and then to Earth. However, Kirk likely meant that he has never been that close to a Klingon Cruiser specifically rather than close to any type of Klingon ship.
After the explosion on Praxis, the shock-wave radiates in a flat plane, even though in space we should expect a spherical propagation (in all directions). Although the filmmakers were obviously more concerned with visual impact than physical correctness, a flat shock-wave is not impossible, if the exploding device had proper dynamical characteristics (and for all we know it might have). Even in nature highly non-spheric explosions do occur. One example is an eruption from a black hole, which propagates in just one dimension (in the form of two polar jets) rather than three.
In the opening scene, Sulu's tea cup faces its printed side toward the camera which looks at Sulu, then Sulu drinks from it, we do not see him place it down. We see the cup next from Sulu's perspective, which is clear because not only is the printed text missing, but the handle is now on the other side. Other than the text and the handle, there is no other reference in either frame to determine which way the cup is facing, so there is no goof.
Rura Pente is supposedly so cold that a person's skin freezes when he is thrown to the ground, yet we do not see the breath of any of the actors.
In the locker room scene, the marks on the locker door where the magnetic boots are supposed to go can be seen (Velcro, painted the color of the locker).
When the Klingon vessel loses gravity and the officer's pistol comes out of its holster, the string pulling the weapon free can be seen.
When Uhura is conversing with the Klingon listening post. The computer screen beside Uhura's head is displaying the real-time translation of the Klingon's dialogue. The scene was changed at the last minute to add comic relief. The special effects team had already made the computer screen animations, and there wasn't time to change them.
In the early scene in Kirk's quarters, the right eyebrow of Lieutenant Valeris becomes loose at the outer tip. The first time it is visible is at the line "Permission to speak freely, sir. It is an honor to serve with you." By her next line, "I've always wanted to try that, sir", the eyebrow has been reaffixed.
Uhura is able to figure out in seconds a way to defeat the Klingon cloaking device that nobody ever managed to work out in the decades since it was put into service. Similarly, when Spock rushes to retrofit a torpedo with conveniently drop-in parts, he doesn't ask engineer Scotty to help him, but McCoy, who has zero engineering knowledge.
When Kirk and McCoy were arrested, McCoy's hands and uniform are clean despite having just given CPR chest compressions to Gorkon while blood pools heavily on his chest.
Both Kirk's and Sulu's quarters are entered by subordinates without being granted access.
In the galley, just as Scotty exits, Spock orders: "Valeris, please inform Starfleet Command that our warp drive is inoperative." Yet Spock's lip movements seem to indicate that the name "Valeris" was dubbed over "Commander Uhura," which would make sense given that the latter is the ship's communications officer and she is standing right there, but was likely changed to match the subsequent dialogue and action: Valeris asks, "A lie?"; Spock replies, "An error"; then Valeris walks away as Spock continues to speak with Uhura.
When Scotty is reporting that the torpedo bay is "fully loaded" during the initial attack, the audio does not match the movements of his mouth in the reflection in the screen.
When Colonel West cuts through the glass and watches the Federation president speaking the speech does not match the president's lips.
On Rura Penthe, McCoy's lips initially aren't moving when he says, "He's definitely on about something, Jim."
At 01:26:19 in the Special Edition, during the scene where Kirk, Spock, and McCoy trick Valeris in the sick bay, a member of the film crew is visible to the side (stage left).
During the assassination scene, after Chancellor Gorkon says "Find Chang!" the shadow of the camera can be seen on the left side of the screen in a shot of some doors opening.
Uhura's lack of knowledge of the Klingon language is at odds with her being Communications officer, since she should at least have some working knowledge of the language of the Federation's greatest rival. She once spent three months effortlessly handling the communications station on board the captured Klingon Bird of Prey in Star Trek IV: The Voyage Home (1986), where all the controls were written in Klingon. (The filmmakers argued about this: see trivia.)
When the Enterprise is shown approaching the planet with Camp Khitomer, there are no other ships or any other activity in orbit around the planet. Given the peace treaty talks taking place with so many VIP's from so many different species in attendance, there should be a considerable number of ships and perhaps even space stations and/or orbital defenses present in orbit around the planet from all species in attendance to protect the conference and its attendees.
Kirk and McCoy are on trial for the death of Chancellor Gorkon. Yet, in Star Trek IV: The Voyage Home (1986), the Klingons were demanding the extradition of Kirk for the death of Commander Kruge and his crew in Star Trek III: The Search for Spock (1984), as well as the theft of a Klingon vessel. These charges are not mentioned at the trial. (The film makers wanted to include this plot element, but couldn't for practical reasons - see trivia.)
There is a call over the intercom for all officers to go to the bridge. It is unlikely all of the officers assigned to Enterprise would fit on the bridge. Also most of the officers would be needed in their assigned spaces.
Colonel West presents the Federation President with a proposal to enter Klingon territory, a plan called "Operation Retrieve" that could provoke a war. In a subsequent scene, the new Klingon Chancellor communicates with the President, and the large mission charts are still beside the President's desk in full view.
Chekov is Security and/or Tactical Officer but somehow doesn't know that firing phasers on board sets off a security alarm.
Valeris quotes Kirk, saying he said to "let them die." Kirk said this to Spock before meeting her, and Spock never tells her about it.
When conferring with Valeris in the ship's galley about the possible whereabouts of the gravity boots, Spock dismisses Valeris' theory that they may have been left on the Klingon ship, explaining that "gravity had not been restored when the assassins beamed away. Without them, they would have floated off the Klingon transporter pads." This seems to indicate that the transporter would not have picked up anything floating around the pad when the transport was initiated.
However, an earlier shot of the assassins beaming off the Klingon ship clearly shows floating Klingon blood dematerializing during transport, and a later scene shows Chekov discovering Klingon blood in the transporter room, indicating that a transporter pad can lock onto floating objects. Therefore, Spock's dismissal of Valeris' theory, although correct, should not have happened out of hand.
However, an earlier shot of the assassins beaming off the Klingon ship clearly shows floating Klingon blood dematerializing during transport, and a later scene shows Chekov discovering Klingon blood in the transporter room, indicating that a transporter pad can lock onto floating objects. Therefore, Spock's dismissal of Valeris' theory, although correct, should not have happened out of hand.
Scotty and Valeris wear two different division colors: Scotty wears a white shirt of the command division and his jacket displays yellow of engineering, possibly because his rank is captain, but he retains his engineering colors on his coat, which would be confusing to crewmen. Valeris has a more unusual uniform, she wears the red shirt of trainees while her rank insignia is lieutenant commander and with gray trim for the operations division, without explanation.
Kirk notes in his Captain's Log that Romulan Ale is no longer to be served at diplomatic functions. As a Klingon rightfully pointed out earlier, Romulan Ale is illegal. Kirk would be admitting in an official document that he violated this law.