Where No Man Has Gone Before - S1-E4
Visible crew/equipment: When Dr. Dehner is talking to Gary Mitchell in sick bay, when he grabs her arm you can see the shadow of the boom mic on the door and adjacent wall. (00:19:25)
Factual error: When they are searching for Finney hidden somewhere in the ship, all ship noises are deadened, and the heartbeats of those on the bridge are muffled by McCoy. In order to locate Finney's heartbeat the ship's auditory sensors are magnified by "one to the fourth power". That's 1x1x1x1 = 1, ie no magnification.
Revealing mistake: In the first illusion, Vina runs down the path from the fortress to Pike. When we cut to close-ups, they're both suddenly standing much closer to the building than before, and the fortress has changed color from brownish orange to white. (00:23:50)
Continuity mistake: Kirk and McCoy are in the Exeter's engineering section when Kirk uses the intercom to ask if anyone is aboard. Several shots of the deserted ship follow as his voice echoes off the walls, including one of engineering - with Kirk and McCoy suddenly, mysteriously absent. (00:03:45)
Continuity mistake: Initially, the Enterprise orbits Psi 2000 as the planet turns westward. But in later shots, on the bridge view screen, the planet has reversed directions and now turns eastward. (00:04:05 - 00:12:00)
What Are Little Girls Made Of? - S1-E8
Continuity mistake: When the android Kirk boards the Enterprise and takes a "command pack," he walks out and down to the transporter, but he doesn't have the pack in his hand.
Continuity mistake: When Kirk is facing the Horta he has his phaser in his right hand when seen from the front but when seen from behind he has his communicator in his left hand and no phaser. (00:31:00 - 00:38:00)
Tomorrow is Yesterday - S1-E20
Continuity mistake: When Kirk and Sulu enter the records room, they pick the lock. Later when they beam the officer back down, he enters the room without unlocking the door. The room should be locked since they beamed him down in the "past" erasing their having been on Earth and in the records room.
Other mistake: Spock records a log entry as the "second officer". It appears they got "first officer" confused with "second in command." (00:36:15)
Revealing mistake: Due to a poor edit, there's an odd jump cut and a change of lighting just as the Keeper comes out of the elevator on his way to an attempt to steal the laser pistols from the cell. (00:50:40)
Is There in Truth No Beauty? - S3-E5
Revealing mistake: During the fight in engineering, Marvick's kick, throwing one of the engineering crewmen violently back against the wall, misses by an obvious mile. (00:20:10)
Plot hole: Because of the magnetic ore on the work clothes of the man who beamed up, the transporter made duplicates of everything put through it, and so couldn't be used. This was further complicated by the control and power circuits being blasted by the "evil" Kirk. However, the ship carries a number of shuttle craft, which no-one mentions.
Continuity mistake: After Spock's Brain is taken McCoy says he has no idea how long the body can last on life support without the brain. Somehow in the following few moments McCoy has established that Mr Spock's Body will die in exactly 24 earth hours. No explanation is given as to how he came up with this figure.
Is There in Truth No Beauty? - S3-E5
Revealing mistake: The colorful nebulae of the energy barrier are showing through the hull of the suddenly-transparent Enterprise as it heads back into the galaxy. (00:37:40)
Revealing mistake: On the surface of Eden, Spock finds Adam dead under a fruit tree. But the corpse's fingers are still moving. (00:45:20)
The Trouble With Tribbles - S2-E15
Continuity mistake: The tribble-inundated Kirk is holding one of the small fur balls in both hands in some shots, but when the camera angle changes, that tribble vanishes and his hands are no longer even close together. (00:40:40)
Shore Leave - S1-E16
Revealing mistake: Near the end of the episode, the heavy chains restraining the "loose" tiger are visible both around his neck and running across the rocks to the right of the shot. (00:42:35)
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.
Continuity mistake: In "Amok Time" Spock described Vulcan mating rituals as "a thing no out-worlder may know" - here he goes on about them with Droxine at some length.
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.