Visible crew/equipment: At the hangar deck, after Kirk introduces Sarek to Spock and McCoy they all step forward, then as Sarek introduces his aides and his wife, the three white tape marks are visible on the floor behind them, where they had been standing. (00:02:15)
Visible crew/equipment: After Amanda tells McCoy about Spock's pet sehlat, when Sarek and Amanda walk away, the actors' multiple white tape marks are visible on the floor, under the table. (00:10:50)
Visible crew/equipment: While Sarek is lying in sickbay, McCoy, Spock, and Kirk discuss the open heart procedure, and when Christine walks over to stand beside Sarek, the white tape mark is visible on the floor where she stands. (00:24:20)
Visible crew/equipment: While Spock and McCoy are discussing the dangers of the experimental drug, when McCoy tells Spock that he can't sanction it, the two white tape marks are visible on the floor. (00:26:30)
Visible crew/equipment: When Kirk regains consciousness in sickbay he asks McCoy about Sarek, and as the camera turns we see the white tape mark on the floor in front of Amanda's feet. (00:35:20)
Visible crew/equipment: The action is shifting back and forth from the bridge where the alien ship is attacking and sickbay where McCoy is operating on Sarek. In two separate takes when the scene shifts to sickbay McCoy is standing at the operating table. I noticed a wisp of smoke rising from McCoy's right side (left side of screen). It appears to be from a cigarette in an ash tray below camera level either beside McCoy or near the head of Spock's bed.
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.