Requiem for Methuselah - S3-E19
Revealing mistake: When Spock examines the unknown Brahms waltz, we get a close-up of the music. Unfortunately, the hand-written score bears no resemblance whatsoever to the piece Spock has just played, though he expressly identifies it as such. (00:19:10)
Requiem for Methuselah - S3-E19
Revealing mistake: As Kirk pulls the shroud away from the Rayna duplicate, look closely at the part of her head just below her left ear. The bald cap she wore to conceal her hair and give her an unfinished look.
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.