Visible crew/equipment: In Kirk's quarters, as the camera goes to a close up on the "evil" Kirk, watch the reflective strip behind him. The movements of the camera are reflected and noticeable.
Visible crew/equipment: On the bridge, Uhura tells Kirk that Outpost 4 reported they're under attack, and after Scott says, "I've talked to my engine room, sir. We'll get more speed out of her," we can see the movement of the overhead boom pole's shadow as Kirk walks toward Uhura.
Space Seed - S1-E23
Visible crew/equipment: When Khan hides behind the wall in the engine room before Kirk enters, a crew member walks in front of the stage light and you can see the shadow of his head passing across the floor.
Operation -- Annihilate! - S1-E30
Visible crew/equipment: When Kirk and the landing party are standing on the transporter pads ready to beam down to planet, the camera pans to the right as the transporter operator stands at the console, and the end of the set is visible with black cables lying on floor. (00:07:15)
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)
Space Seed - S1-E23
Visible crew/equipment: When the landing party are aboard the Botany Bay talking about it being a sleeper ship, Kirk asks if it's possible they're still alive, and as the camera follows Kirk the shadow of the camera/cameraman is visible on the wall, at the right side of the screen. (00:06:25)
The Return of the Archons - S1-E22
Visible crew/equipment: After Scotty tells Kirk that the shields are unable to deflect the heat beams, the piercing soundwaves knock everyone out, and when Kirk awakens in the cell he tries to wake Spock, then the shadow of the camera is visible on the pillar as it follows Kirk. (00:25:55)
Visible crew/equipment: When the Metron returns Kirk to the Enterprise he reappears on the bridge, and the actors' chalk marks are visible on the floor where Kirk and crew stand. (00:47:20)
The Corbomite Maneuver - S1-E11
Visible crew/equipment: After the Fesarius destroys the recorder marker, when Balok declares that Enterprise must also be destroyed, in the next wide shot two tape marks are visible on the floor, one in front of Kirk's feet and another near Bailey. (00:21:50)
Where No Man Has Gone Before - S1-E4
Visible crew/equipment: While Kirk is armed with a phaser rifle he quietly moves closer to Gary and Dr. Dehner, but when Gary senses the "foolish man" he causes a boulder to roll past Kirk, and the arm of a crew member is visible behind the boulder pushing it forward. (00:39:40)
Where No Man Has Gone Before - S1-E4
Visible crew/equipment: While Kirk, Spock, and Dr. Dehner are with Gary in sickbay, when Gary makes threatening remarks and gets out of his bed, the shadow of the moving boom mic is visible on the wall at the left side of the screen. (00:28:55)
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.
Visible crew/equipment: As Kirk goes to talk to Uhura, the studio light is reflected of the second to left panel from Uhura.
Mudd's Women - S1-E7
Visible crew/equipment: In the briefing room, as the camera moves to its left along the seated figures, the camera rig is reflected in the glass of the communication view screen.
Where No Man Has Gone Before - S1-E4
Visible crew/equipment: As the camera is close up on Kirk, and as he addresses the ship, the shadow of the boom mike plays on Smith's neck. (00:04:35)
Tomorrow is Yesterday - S1-E20
Visible crew/equipment: When Kirk hears the audio for the first manned moon shot, he gets up to walk over to Spock. As the camera pans to follow, the shadow of the boom mike can be seen moving quickly above and to the left of his head.
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.