Corrected entry: When Kirk hijacks the USS Enterprise from space dock, Captain Styles gives pursuit in the USS Excelsior, and Styles radios a warning to Kirk: "If you do this, you'll never sit in a captain's chair again!" Of course, Kirk is a Starfleet Admiral, not a captain, so sitting in a captain's chair is the least of Kirk's concerns.
Corrected entry: During the opening sequence, you can see a highway with cars driving in the bottom left-hand corner of one of the scenes.
Correction: No, you can't. It was filmed at a park in California (with additional prop plants and a smoke machine). It is a stream and the 'cars' are the rocks underneath the moving water.
Corrected entry: When Kirk, McCoy and Sulu beam aboard the Enterprise we switch to an outside shot and the bridge lights come on, a very bright white light that lights up all three windows, but when we go inside the bridge is very dark with only a few lights on. The main lights come on when they man their stations.
Correction: What is being described are not 3 windows, they are 3 lights for lighting up the ship's registry and name. There are no windows in a Constitution class' Bridge, original or refit.
Corrected entry: When Uhura is holding "Mr. Adventure" at phaser point to let Kirk McCoy and Sulu get away, after she says "This is fantasy!", she is holding the phaser level and steady. As the shot turns to him, watch her hand. It tilts over to her right by about 60 degrees. When the shot goes back to her, it's straight up again.
Correction: This isn't a mistake, she is taunting him with the phaser for the "career winding down" crack. She has time to snap it back up before the camera comes back. It would take less than a second.
Corrected entry: During the Klingon's first scene, the cargo ship noticeably increases in size. As the Bird-of-Prey decloaks above it, the Bird-of-Prey is considerably larger. When the Klingon vessel comes around to destroy it, the cargo ship is now LARGER than the Bird-of-Prey.
Correction: It's a matter of perspective: the Bird of Prey is closer to the camera in the first shot, thus making it appear larger.
Corrected entry: At night on the Genesis planet David, Saavik and young Spock are braving a raging storm. You can see a tree fall over and clearly land on a Klingon. Problem is David, Saavik and Spock have not encountered the Klingons yet.
Correction: The Klingons haven't found Saavik, David, and Spock yet, but they are on the planet looking for them. Since the storm is raging all over the planet, it is logical to assume that the Klingons are getting hit by the same storm in a different area.
Corrected entry: Chekov's clothes change after the Enterprise leaves the Spacedock facility. It was unlikely that he would have taken the time to change his clothes during a moment of crisis.
Correction: After escaping from Spacedock, Chekov had little to do for the several hours it took to reach Genesis, giving him ample time to change his outfit.
Corrected entry: In the star trek universe, NX stands for New eXperiment for prototypes. You see many examples of this including Deep Space 9's USS Defiant NX 74205, and NCC stands for Naval Construction Contract (number), which is everywhere else. Once a ship has been moved out of the prototype phase it is assigned NCC, as are all subsequent vessels of the same class.
Correction: Official material has never given an explanation for the meanings of "NX" or "NCC." The trivia you repeat is popular in fandom, but it is in no way official. Please see articles such as http://www.ex-astris-scientia.org/inconsistencies/false_canon.htm for an explanation of this phenomenon.
Corrected entry: How did the captain of the Excelsior know that it was Adm. Kirk that was stealing the Enterprise? Never once was he informed who it was taking the ship.
Correction: Just because we don't see him actually being told, it doesn't mean that he wasn't informed, off-camera. The moment it became apparent that the Enterprise was being stolen, Starfleet would have been investigating to work out who was responsible - given that Kirk's already asked if he can take the ship, it wouldn't take much to work out who was behind the theft, and they would have informed the Excelsior immediately. Styles would have had the information given to him the moment he reached the bridge.
Corrected entry: When the Enterprise self destruct sequence countdown reaches zero, it goes through an elaborate destruct sequence that tears the ship apart and sends the remains plummeting into the atmosphere of the Genesis Planet. Star Trek producers have said that auto-destruct systems involve an intentional release of the matter and anti-matter fuel. This would cause the ship to go up in a sun-like fireball, and there wouldn't be very much wreckage left - certainly not the amount of wreckage seen in the film.
Correction: According to Mr Scott's Guide to the Enterprise (a movie supplement released just after STIV) if the final code is given as "Destruct Zero" (which Kirk does), charges built into the hull, engines and computer will render the ship a useless hulk, making it pointless to capture. If the code used is "Destruct One" the matter-antimatter mix overload is used. Destruct One is for use in deep space where the antimatter explosion won't harm planets or ships nearby.
Corrected entry: As Saavik and David are scanning the Genesis planet, the readout on their computer screen says CELCIUS - 'Celsius' misspelled. The camera zooms in to give you a nice close look.
Correction: [It may be hard to read due to the font size, but Celsius is spelled correctly. The chosen type face and the screen resolution make the "S" look like a "G" or "C" but it is a lower case "S".]
Corrected entry: We see Excelsior has the hull number MKT-2000. The only other prefix we have seen in Star Trek is NX for prototype vessels. Given the experimental drive, she should have been NX-2000. What is MKT? And why is she NCC-2000 in Star Trek VI?
Correction: The hull number of the Excelsior can be seen to be NX-2000 at least three times in the movie. On the Special Collector's Edition DVD NX-2000 can be seen at 0:12:37, 0:43:46, and 0:46:42. NX-2000 can be seen in the VHS version as well. An MKT-2000 is nowhere to be seen. The hull number is again NX-2000 in Star Trek IV: The Voyage Home. Only in Star Trek VI: The Undiscovered Country is the hull number NCC-2000. Presumably the ship is no longer a prototype at that point.
Correction: Captain Styles is basically saying that Kirk will be court marshalled if he carries on with stealing the Enterprise.