Other mistake: During the inquiry at the start of the movie, the Klingon Ambassador is going over the footage of the destruction of the Enterprise from all the exterior views. This is very nice, but how would they have access to all of these different viewpoints of the destruction? Bearing in mind no-one was there to film it. It couldn't have been the Klingon Bird of Prey that filmed it, because in most of the destruction scenes, the Bird of Prey would have been no-where near or in a position to film it, and was of course captured and still being commanded by Kirk during the course of the inquiry. (00:04:10)
Suggested correction: Most of the visuals we see on view screens in Star Trek are created from sensors rather than cameras, so what we see doesn't necessarily have to be from the visual perspective of the ship taking it. Though yes, it is quite an amusing coincidence that it all looks exactly like they're watching a copy of Star Trek III on home video.
Suggested correction: It's possible the Grissom and/or the Bird of Prey launched drones into orbit to aid in the scanning of the planet or for communications or sensor relays, and this is where the footage could have come from. This isn't unlike the beginning of Star Trek: The Motion Picture, in which crewmembers of the space station mentioned such drones as the reason images of the aftermath of the V'ger destruction were able to be seen despite no ships being left.
Other mistake: When Kirk sells his "18th Century" reading glasses, a close-up reaveals that the ends of the stems are made of clear plastic- not possible in the 1700s. (00:40:55)
Visible crew/equipment: During a close up of the police officer's sunglasses, when Chekhov is asking for directions to Alameda, some crew are visible in the left lens. They are a line of people trying to stay out of the camera. (00:43:30)
Visible crew/equipment: During the scene on the bus, two members of the camera crew are visible in the window behind and to the right of Spock. The crewman of the left is sitting and operating the movie camera, and the crewman on the right is taking still camera shots. (00:43:50)
Factual error: When Chekov and Uhura first see USS Enterprise and then later beam aboard, the carrier shown is not USS Enterprise (a nuclear aircraft carrier), but rather USS Ranger (a conventional or oil-fired carrier). The most obvious clue is the "island", the huge structure that sits on the deck of the carrier. USS Enterprise has the most distinctive and unique island of all the USN carriers, being totally cube-like in appearance. The carrier in Star Trek IV has a more conventional style island. [It is true that the USS Ranger was used in lieu of the USS Enterprise for the movie. This is because the Enterprise was on deployment at the time. Though by the time the movie was made the Enterprise had had its distinctive pagoda-like island rebuilt by Puget Sound Naval Shipyard in 1980, the aircraft carrier served until 2012 with a still-distinctive cube shaped island.] (00:53:30)
Continuity mistake: Gillian's Chevrolet pick-up truck is obviously two different trucks, depending on its location. When near the aquarium, the grille is a series of large, rectangular openings. But when at the park, where the Bird of Prey landed, the grille is a much tighter series of more numerous, smaller rectangles, made up of much thinner bars. This difference is consistent through the entire film. (00:55:05)
Continuity mistake: In the scene where Kirk and Spock are walking down the street after Spock has been in the tank with the whales it is clear that it is a windy day. Both of them have their hair blowing in the wind and yet as they are offered a ride in the truck and the shot leaves them for a moment their hair is suddenly fixed again. (00:55:20)
Audio problem: When Gilliam slams on the brakes, the tires make a screeching sound, but the wheels come rolling to a stop, ergo do not skid. (00:56:50)
Continuity mistake: Notice the candle on the table in the Italian restaurant scene during Capt. Kirk and Dr. Gillian dialog. It changes height depending who is talking. (01:03:50 - 01:08:30)
Factual error: The nuke ETs are sitting at a RADAR station, not a power output monitoring station. The RADAR wouldn't give any sort of indication of sudden additional power draw on the reactor. (01:12:00)
Visible crew/equipment: In the scene where Mr. Chekhov is being interrogated on the USS Enterprise (the aircraft carrier) after being caught on board, a studio microphone being used for the shot is visible hanging above him. (01:14:45)
Visible crew/equipment: In the scene where Sulu flies the helicopter and accidentally turns on the windshield wiper, look closely at the bottom of the wiper and you can see the crewman's finger manually moving the wiper. (01:18:55)
Factual error: They are about to perform major brain surgery on Chekov, but he is not nearly prepped for such a procedure. His head is not shaved, the area is not marked or masked and it has not been swabbed with Betadine, even though they are about to cut into his skull with a bonesaw. The "they haven't had time to prepare yet" argument doesn't hold water, because the surgeon is already approaching Chekov's head with the saw. (01:24:30)
Other mistake: When Kirk uses his hand phaser to melt the lock on the door in the hospital operating room, the phaser is not pointed directly at the lock. The beam leaves the phaser at an angle, which is probably not how the phaser would have been designed to operate. (01:25:20)
Continuity mistake: In the operating room, when Kirk uses a phaser to melt the lock, the hand he is holding the phaser in switches hands in the closeup shot. Additionally, the arm holding the weapon in the closeup is no longer in hospital scrubs, but a similarly colored sweatshirt. (01:25:20)
Visible crew/equipment: At approximately 01:32:50 on the Blu-Ray, you can see a diver releasing the mechanical whales. He is on the far right side of the screen, you can make out his head, body and left hand. He is visible for a good 8-9 seconds. If you have a different media source, it's during the Bird of Prey decent. You see a closeup of Kirk, followed by a closeup of Uhura and Gillian, then a close up looking down on the harpoon. It's in the following scene. (01:32:50)
Continuity mistake: When the 'Bounty' materializes right above the whaling ship, it casts it into shadow. But the close-ups of the captain and navigator as they frantically turn the ship around reveal no trace of a deeper shadow on their faces and the surrounding waters; the lighting remains the same as in the scenes when they try to catch the whales. (01:33:45)
Revealing mistake: When the whales first swim past the now submerged Klingon Bird of Prey, if you look to the right where the water is supposed to meet the distant horizon, you can see an exposed edge to the 'horizon' as the water moves up and down. This is the edge of the pool they are in, and the exposed edge is the bottom of the painting of the sky behind them. (01:46:30)
Factual error: Scotty is listed in the credits as Captain Montgomery Scott. At the end when the camera pans the crew just before their pardon, Scotty wears the rank pin of a Commander (the same one worn by Commander Sulu, Commander Chekhov, and Commander Uhura). (01:48:55)
Other mistake: After they take off from California, Kirk gives a heading to Alaska. He then tells Sulu "full impulse power", and Sulu says "aye, ETA 12 minutes." Full impulse is 1/4 the speed of light. No way they would use speeds like that to go a few thousand miles.