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.
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 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)
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)
Other mistake: When we first see the Klingon bird of prey on Vulcan (just before we see closeups of the "Bounty" written on the side) it is clear that the ship is far too small to contain a pair of adult humpback whales plus 18000 cubic feet of water in its hold. Later, when the ship is hovering above the sea after foiling the whaling ship's attack it seems considerably larger.
