The Conscience of the King - S1-E14
Visible crew/equipment: When Lenore arrives at the Leighton's cocktail party, there is no furniture behind Kirk in the center of the room where they will stand in a moment. When Kirk introduces himself, in the next three shots facing Lenore, in front of her arm we can see a bit of camera equipment at the bottom of the screen.
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.