Continuity mistake: The shards of the goblet Spock breaks change quantity and position on the table with the fruit bowl on it. (00:28:30 - 00:31:30)
Continuity mistake: Just before Parmen starts mind-controlling Kirk, McCoy and Spock, he presents them with three gifts. Kirk receives a large, gold Greek shield, which the captain holds with both hands, in front of him, as the lengthy scene continues. In the wide shot, Kirk is holding the shield high up on his chest, completely obscuring his Federation insignia. In subsequent close-ups, Kirk is holding the shield down low, around waist-level, fully exposing his chest and insignia. Every time the camera cuts back to wide-shot, Kirk is again holding the shield up high on his chest.
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.