Visible crew/equipment: After Spock has jettisoned Galileo's fuel and ignited it, when it cuts to the bridge aboard Enterprise the shadow of the camera/equipment can be seen moving across the helm console.
Visible crew/equipment: After Spock asks Scotty if there's enough battery power to electrify the exterior of the ship, Spock tells everyone, "Get to the center of the ship. Don't touch the plates. Be sure you're insulated," and just as Spock turns in the rear compartment we can see the edge of the shuttlecraft set behind Spock.
Visible crew/equipment: As the camera swings around to simulate the crewman's gaze, the top of the background is visible for a second until the camera pans down.
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.