Continuity mistake: As Kirk speaks with Commisioner Ferris, Kirk's hands go from holding a piece of equipment to being straight down by his side, back to holding the equipment.
A Taste of Armageddon - S1-E24
Plot hole: The ambassador and his aide beam down to the planet. This would not be possible because earlier on Scotty refused to lower the screens/shields until the Captain told him to do so. It had already been established in an earlier episode titled "Arena" that transporters don't work with screens up. (00:32:40)
Factual error: Trelane has been watching Earth as it was 900 years ago (14th century in the film), but his style is more 17th century, and he mentions Napoleon who lived in the 19th century.
This Side of Paradise - S1-E25
Continuity mistake: When Kirk and Spock successfully activate a subsonic transmitter, it cuts to a closeup of a spade's metal blade breaking the soil ground, but in the next wide shot Sulu and DeSalle are using two spades made entirely of wood. (00:44:45)
Revealing mistake: When Kirk and Miri are in the kid's hideout, Kirk is attacked by Louise, the wild woman. After Kirk knocks her off his back, she falls to the ground and tries to get up again, Kirk has to resort to stunning her with his phaser. The blue beam starts coming out then starts coming back towards the phaser before going back out again. (00:26:12)
Tomorrow is Yesterday - S1-E20
Revealing mistake: Traveling towards the Sun and away from the Earth, parts of the Enterprise are missing due to superimposing the model into the current shot. As the Enterprise goes by, one of the warp engines seems to be disintegrating at the rear. (00:42:05)
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)
Continuity mistake: After McCoy checks the Horta, he approaches Kirk with his tricorder in his left hand. The scene cuts to McCoy and Kirk and now McCoy's tricorder is in his right hand.
Continuity mistake: Spock and Kirk both arrive at the sizzling remains of a red shirt crewman, standing close together, but the next shot of the crewman's remains shows only one set of legs at the site (presumably Spock's), not two.
Revealing mistake: As Spock carries the crewman, the second spear hits a rock. As it does, you can see the Styrofoam chips fly up.
Factual error: The harpsichord Trelane plays is far too short and has pedals like a piano.
Other mistake: Ben Finney's rank is stated as Lt. Commander. His rank insignia on his uniform shirt is that of Commander (The same as Mr. Spock whose rank is Commander).
Visible crew/equipment: As Spock swings the scanner around, as it points toward the camera position, the camera equipment is reflected on the chrome plate on the front.
Other mistake: When the nuclear bomb explodes, the ship is tilted 40° to 45° to starboard (right), but Uhura goes over to the port (left) side of the lift.
Revealing mistake: As the Romulan ship is tilted, the dust and debris fall straight down, rather than diagonally toward the wall and floor joint.
What Are Little Girls Made Of? - S1-E8
Revealing mistake: When Korby introduces the new android Kirk to Chapel, as the duplicator table slowly turns the edit in the footage can be seen in this shot, just as the real Kirk suddenly vanishes from the space he was in.
Visible crew/equipment: When Spock walks into the briefing room, he stands in front of the closed doors telling himself that he's in control of his emotions, and when he says, "My duty," the shadow of the boom mic can be seen moving across the wall at the top of the screen. (00:36:40)
Tomorrow is Yesterday - S1-E20
Character mistake: When first considering the impact of Captain Christopher's removal from this time, Spock makes a mistake in his dialogue. He says "They show no record of any irrelevent contribution..." when it should be "relevent..." (00:13:50)
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)
Revealing mistake: After Spock finds Gaetano's body he carries him back to the shuttle, and in the interior shot as McCoy and Boma carry Gaetano's body to the back, we can see though the shuttlecraft's doorway the top of the set's blue backdrop.
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.