The Return of the Archons - S1-E22
Other mistake: On the bridge, as the camera looks at the view screen, there is a flashing blue light reflecting on the console in front of Sulu, but there is no light other than scanner under the viewer flashing and it's too far away to project light that far, and it's amber colored.
The Return of the Archons - S1-E22
Continuity mistake: As Marpon talks to Spock, his right hand goes from being palm forward toward Spock, to being vertical, palm open, thumb upwards, and back.
The Return of the Archons - S1-E22
Revealing mistake: In the holding cell, as Spock attempts to analyze McCoy's mental state, the alcove is brightly lit a hand held lamp. As the camera pulls back, the light is seen to move, and then is turned off.
The Return of the Archons - S1-E22
Continuity mistake: As Kirk talks to an "absorbed" McCoy, in the back-and-forth cuts between them, the part in Kirk's hair jumps from left to right and back.
The Return of the Archons - S1-E22
Continuity mistake: While Kirk is attempting to convince Marplon and Reger to take them to Landru, a distant shot shows Marplon's right hand descend from his chest to his side. Immediately thereafter, a close-up shows Marplon's hand again suddenly at his chest.
Space Seed - S1-E23
Continuity mistake: When the landing party beams over at the beginning, the transporting officer is wearing a blue jumpsuit, but when they go to the closeup of his hands, they have a red uniform, two braid stripes, and are the standard shot they use when Scotty does the transporting. (00:05:05)
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
Continuity mistake: At the hearing in the final scene, there are two bits of debris of some sort (small, black and roundish) littering the floor at the bottom left of the screen. Whatever it was disappears when Scott, Spock, Kirk and McCoy get up to leave the room. (00:48:20)
Space Seed - S1-E23
Plot hole: It is stated during the episode that Khan was, at one time, the ruler of over 1/4th the Earth's population, during a very key moment in the planet's history (The "Eugenics" Wars). Such a personage undoubtedly would be very well known to 23rd century Earth people, at a level of infamy approximating Julius Caeser or Adolf Hitler. Yet it is only 2/3rds the way through the episode, thanks to a computer search by Spock, that the crew divines his identity. Lt. McGivers at the very least should have almost instantly recognized him.
Space Seed - S1-E23
Other mistake: Spock calls for McGivers and Scotty to the transporter room. In the Transporter Room, Scotty is at the controls, then after he went to the Transporter pad, they used a stock shot of his hands working the controls.
Space Seed - S1-E23
Revealing mistake: During the fight sequence between Kirk and Khan in the engine room, you can see in some shots that it is not William Shatner and Ricardo Montalban fighting, but their stunt doubles.
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.
Space Seed - S1-E23
Continuity mistake: As the away team observes Khan in the stasis chamber, McCoy holds his tricorder with both hands, but the next shot shows him holding it in one hand.
Space Seed - S1-E23
Continuity mistake: On the Botany Bay, McCoy is not holding his tricorder, but when the ship's lights activate, McCoy suddenly has his tricorder in his hands.
Space Seed - S1-E23
Continuity mistake: When Khan asks Kirk "How long?" Kirk's head is near Khan's with nobody behind his head, but the next long shot shows Scotty behind Khan.
Space Seed - S1-E23
Continuity mistake: Khan's hands switch positions several times on the table between quick cuts as he and Kirk talk.
Space Seed - S1-E23
Continuity mistake: At the compression chamber, the pressure meter goes from thirty to ten too quickly to be accurate between shots. After showing ten, the meter jumps back to twenty.
Space Seed - S1-E23
Revealing mistake: Just before Kirk and Khan fight in Engineering, Khan bends Kirk's phaser pistol in half, but the small hand phaser on top is still functional.
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)
A Taste of Armageddon - S1-E24
Continuity mistake: Just after the ship is first attacked, Scotty tells McCoy, "We can't fire full phasers with our screens up." Say what? The Enterprise couldn't operate transporters with the shields up, but it fired its phasers, full or otherwise, with the screens up every time it went into battle, and always had. If they'd been forced to shut their shields down every time they fired, the Enterprise would have been history long before this. (00:23:30)
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.