Continuity mistake: While Flavius guides Kirk, Spock, and McCoy to the city to find Merik, the foursome stop behind a group of trees. In the first wide shot, as Flavius explains they'll wait until dark, there are no red marks on the tree trunks, but in their closeups there are a few red marks (presumably from squibs), before the gunfire has even occurred. At the start of the second wide shot the tree trunks are still void of those marks, and when the police shoot at them that's when the red marks appear. (00:15:15)
Continuity mistake: While Kirk, Spock, and McCoy attempt to escape, Merik contacts Enterprise with the stolen communicator and the Proconsul stabs him, then when Merik tosses the communicator it lands in front of Kirk's feet in a closeup. The problem is that in the closeup Kirk is wearing his black uniform pants, but during this scene Kirk is wearing the light colored slave pants. Also interesting to note, when the sword landed on the floor in front of Spock's feet, the Vulcan is wearing black lace-up flat footwear instead of his black uniform boots. (00:46:35)
Continuity mistake: After Spock talks about Sun Worship on the bridge, Uhura goes to correct him. As she's sitting at her console, her arm is covering the note board. When the angle changes to include her, Kirk, Spock and McCoy, her arm is above the note board. Back to a close up, and her arm's covering it again.
Continuity mistake: When Kirk, Bones and Spock are commanded to stop, and raise their hands, they do so. After a moment, Kirk starts to lower his hands. After the camera cuts to a shot from behind, Kirk's hands are by his sides and he goes for his phaser. After another warning shot, he says "I think he means it." The camera goes back to facing them, and his hands are up again.
Continuity mistake: The chain symbol on Kirk's shirt goes from dark to light and back several times.
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.