Continuity mistake: When Sulu confronts the men in the corridor, his epee goes from perfectly straight to having a slight crook, then back to straight when he appears on the bridge.
Continuity mistake: As Joe draws back and stands up, he pulls a knife. First, it's sharp side up, then it's suddenly blade down.
Continuity mistake: The background of the cell does not jibe with the positions of Kirk and Cloud William as they fight - where Kirk and Cloud William should have either the cell's bars or the exposed brick wall behind them, there are shots of the opposite wall behind them instead, which is a plastered rock facing.
Visible crew/equipment: The shadow of a boom mic is seen against the rock walls of the cave follows Spock and McCoy when Spock pulls McCoy off Zarabeth.
Revealing mistake: When Mr Hengist goes on the rampage in the hearing room, you can see that the actor playing Hengist is an obvious stunt double wearing a bald cap, whereas John Fiedler has hair on the back and sides.
Requiem for Methuselah - S3-E19
Continuity mistake: When looking at the view screen from the helm, there is a man sitting at the Conn position, but in the wide angle, there's a woman there.
Requiem for Methuselah - S3-E19
Other mistake: If the ship had not been in visual communication, there's no way Kirk could have seen the Bridge or the crew in suspension.
Continuity mistake: As Nomad first hears Uhura's singing, it extends antennae and leaves the room. After a quick cut scene, as it turns in the corridor the antennae is retracted, then out again on the bridge.
Continuity mistake: In the original version, the planet is the same as the one used in "Bread and Circuses", but when the Enterprise leaves orbit at the end, it is a totally different planet, as it is the one used in "Friday's Child".
Continuity mistake: When the Enterprise is trying to push away the asteroid using the deflector, a quick shot of Uhura is shown from stock footage of "And the Children Shall Lead," but she is not in the rest of the episode.
Tomorrow is Yesterday - S1-E20
Other mistake: The Air Force police officer (played by Hal Lynch) was beamed up from inside the records room (after finding Kirk exiting the dark-room) but was returned outside the room... so he was physically transported INTO himself (as opposed to replacing the beamed-up future version at the exact moment and place he was removed as they did the pilot, Christopher).
The City on the Edge of Forever - S1-E29
Factual error: When Edith Keeler is killed by the truck, it is traveling at about 25 miles per hour. At that speed and her weight around 120 pounds, she would have been thrown about 50 feet. However, she's seen dead on the ground in front of the mission where she was hit.
The Conscience of the King - S1-E14
Plot hole: After Kirk sees Leighton laying next to the rocks, he rushes over to examine him. He places one hand on Leighton's arm and the other on Leighton's waist and declares "It's Tom Leighton...he's dead." All this without the use of a medical tricorder or even the experienced opinion of the ship's doctor to confirm what Kirk is seeing. (00:10:46)
Other mistake: The only way to beam up to the ship is to repeat the chess counter move after ASKING to be beamed aboard. After the two Captain Kirks fight ends with Spock stunning Garth with the phaser, Spock contacts the Enterprise. After saying "Spock to Enterprise, and hearing Scotty say back to him "Scott here", Scotty says" Queen to Queen's level 3" without Spock requesting to be beamed aboard or even waiting to see what Spock wanted in the first place. (00:46:56)
Other mistake: Stiles gives a countdown for impact to Kirk saying "estimate it will overtake us in two minutes, sir." After only 31 seconds, Sulu starts his own countdown, saying "5, 4, 3, 2, 1, impact." Only 55 seconds have passed from the time Stiles started his countdown to actual impact. Everything was shot in real time without scene changes. Being off the impact estimate time by over a minute doesn't sit well considering a Starship's advanced sensors. (00:29:27)
Continuity mistake: Kirk turns his head and displays a stunned look... a full second before the Gorn even starts to disappear. (00:45:47)
Revealing mistake: As Scotty is cutting through the wall, the line where the burn is supposed to go is outlined on the inside of the wall.
Continuity mistake: At the end, on the Bridge, when the warning marker explodes, Kirk's arm shifts position between shots.
Continuity mistake: When Scotty inhales the gas, the amount of smoke changes between shots.
The Man Trap - S1-E2
Other mistake: Sulu is asking Janice why people call inanimate objects "she"? Then gives an example. He says "Like, she's a fast ship." But the subtitles get this wrong and have him saying "Like, she's a bad ship". (00:23:30)
Answer: After causing Norman to overload, all of the other androids shut down. The same could be said for the androids on the Enterprise.