Continuity mistake: Kirk and McCoy are in the Exeter's engineering section when Kirk uses the intercom to ask if anyone is aboard. Several shots of the deserted ship follow as his voice echoes off the walls, including one of engineering - with Kirk and McCoy suddenly, mysteriously absent.
Factual error: Spock presents himself to Dr. McCoy in sickbay to be relieved of duty for "killing" Captain Kirk. However, as a medical officer, Bones has no place in the ship's chain of command. Doctors have an officer's rank in recognition of their education and value to the service, but no authority over military matters. (For example should Kirk, Spock and Scotty be indisposed, command of the ship would fall to Sulu who is in the chain of command even though McCoy has a higher rank) If Spock believes he should be relieved for breaking regulations and committing murder, and thus confined until court-martial, Scotty would be the one to do it, as he is the next senior officer. And this is not a character mistake, Spock quotes regulations regularly, there is no way he'd ignore chain of command. Contrary to what viewers seem to think, militaries have regulations and officers don't get to ignore them and do what they feel like! The only reason Spock talks to McCoy is so Kirk can walk out of the back of sickbay and create a nice emotional moment.
Add timeGrumpy Scot
Continuity mistake: When Kirk sits down to consult the computer, the big green potted plant on the shelf behind him is there in full shots and missing in close-ups. It's much too large to be completely hidden behind him: if it shows up behind his head in full shot, it should show in close-ups, too, but it doesn't. It's not there.
Continuity mistake: In the briefing room, Hengist and the Prefect are sitting in chairs against the wall at least a foot apart, with bright overhead lighting that casts no shadows on the wall behind them. When we cut to a two-shot of them, however, they're suddenly shoulder-to-shoulder with almost no space between them, and the lighting changes to cast very dark shadows behind them.