Revealing mistake: During the Court Martial scene, a directorial error led to Kirk's exit from the briefing room in the wrong direction. He walks off screen into what would have been a solid wall or corner. The briefing room's only door is on the other side of the room. (00:39:15)
Continuity mistake: During Spock's Court Martial, Chekov says that General Order 4 is the only exception to Starfleet's no-death-penalty policy, and Sulu and the others agree. However, according to "The Menagerie," that exception is General Order 7, not 4.
Revealing mistake: For the final time in "Star Trek's" 3-season run, Chekov mysteriously vanishes from the bridge to be replaced by that tall blond doppelganger, thanks to an old piece of 1st season stock footage used for the special effects insertion of the view screen. The costumes are also noticeably different from 3rd season's uniforms. (00:14:05)
Continuity mistake: Lt. Galloway, who was killed off the season before in "The Omega Glory," is resurrected without explanation for this final episode. (00:24:25)
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.