A Taste of Armageddon - S1-E24
Visible crew/equipment: When Mea 3 escorts Kirk and his landing party to Anan 7 and members of the High Council, while the group enters the room the actors' marks are visible on the black rug, as they all stand at their marks. (00:06:55)
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.