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.
Visible crew/equipment: As Kirk goes to talk to Uhura, the studio light is reflected of the second to left panel from Uhura.
Shore Leave - S1-E16
Visible crew/equipment: While Kirk is with Spock, when Finnegan shows up again Jimmy boy gives in to the chase, then as Finnegan runs and shouts, "Here I am," the shadow of the camera equipment is visible at the bottom right side of the screen, as it follows Finnegan. (00:35:55)
Shore Leave - S1-E16
Visible crew/equipment: You can see the shadow of a boom mic moving on a tree just as the Caretaker appears. (00:44:05)
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.
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)
Tomorrow is Yesterday - S1-E20
Visible crew/equipment: As Spock gives his report to Kirk on the bridge, the shadow of the boom mic is over his right shoulder. (00:03:35)
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.
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)
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)
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.
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)
Visible crew/equipment: After the Klingon vessel's attack on the Enterprise, while returning fire just as Kirk orders to maintain firing range at 100% dispersal pattern, the set's unfinished wood plank with grey paint drip marks can be seen at the bottom of the screen. Additionally, at the end when Spock goes to stand beside Kirk's chair (also when he walks away) the actor's mark can be seen on the floor by Spock's feet.
Visible crew/equipment: When Kirk is thrown into jail with Spock you can see the movement of the entire blue crash mat used to break his fall.
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)
Operation -- Annihilate! - S1-E30
Visible crew/equipment: When Spock and McCoy walk into Kirk's quarters, in the wideshot the white tape mark can be seen on the floor under the desk at Spock's feet, before Spock requests permission to beam down to the planet, and can be seen again when Kirk stands up.
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.