Is There in Truth No Beauty? - S3-E5
Continuity mistake: At the dinner for Miranda, Kirk drains his glass. No one refills it, but it's nearly full again a few shots later. (00:08:25 - 00:10:35)
Suggested correction: Kirk's glass is not empty at 8:25, it is the top of the decanter in front of his chest that looks like an empty glass in the shot. Later Kirk empties his glass during toasts and refills his own glass as he watches Marvik leave the room.
Continuity mistake: When Scotty thwarts Garth, disguised as Kirk, attempts to beam to the Enterprise using the Queen-to-Queen level three code, Kirk throws a tantrum and accidentally loosens one of his controls during his rant right before he turns back to Garth.
Suggested correction: How is that a mistake?
Trivia: Although James Doohan's voice is heard over a communicator, he is never actually seen in the episode.
Suggested correction: Stating the obvious is hardly trivia. This is also not the only episode where members of the crew are seen but not heard.
I never knew that! While obvious if you watch the episode itself, bear in mind lots of this is just read by people browsing, reading for background info, not necessarily people watching the show, or who've seen the episode in question.
Other mistake: The time that Kirk winds up in doesn't look anything like the what he was viewing on the disk.
Suggested correction: The entire planet isn't going to look exactly like what he saw on the disk. The disk will show random scenes to give the viewer an idea, but we can't expect the whole planet to match that image.
Requiem for Methuselah - S3-E19
Factual error: Spock plays a piece on a harpsichord that he says is by Brahms, but Brahms was a late romantic composer and the piece is a simple baroque dance piece. Also by the time of Brahms the harpsichord was already obsolete, a composition like this wouldn't be sitting on a harpsichord.
Suggested correction: The first sentence is logical; if Spock is able to recognize the style as Brahms, then it should not possess the style and structure of Baroque music. The second sentence is not necessarily true because some romantic composers did write for the harpsichord. For instance, the late romantic composer Richard Strauss composed, "Divertimento for Chamber Orchestra after Keyboard Pieces by Couperin", which is scored with a harpsichord part.