Deliberate mistake: Special effects of the ship in space were very expensive in the 60s and couldn't be wasted. So when a larger model was built with slightly different nacelles, shots of both versions became common, even within the same episode. This is why the Enterprise sometimes had red needle-tipped nacelles and sometimes lighted "spinning" ones, and in aft views she had either round white spheres or perforated vents at the nacelles' ends.
Revealing mistake: While the interior sets for the shuttle craft provided adequate room for the actors to stand, the mock-up built for exterior shots was undersized, and too short to stand up in by several inches. So when entering or exiting the shuttle, the actors always had to duck.
Factual error: In several episodes, when the Enterprise has to turn "hard about", we see it banking to one side like a jet plane. The Enterprise has no wings, and they're in space. No banking.
Visible crew/equipment: As the camera looks at the Galileo, if you look at the green background, you can see the top of the sound stage.
Other mistake: The closing credits of thirteen episodes in season 1 have the word "Script" misspelled as "Scpipt" for the episode's script supervisor, either George Rutter or Billy Vernon. The episodes are: "The Galileo Seven"; "The Squire of Gothos"; "Arena"; "Tomorrow is Yesterday"; "The Return of the Archons"; "Space Seed"; "A Taste of Armageddon"; "This Side of Paradise"; "Devil in the Dark"; "Errand of Mercy"; "The Alternative Factor"; "The City on the Edge of Forever"; "Operation - Annihilate!"
Visible crew/equipment: When the doctor is mixing the drink and Pike gets up off the bed to accept it, an equipment shadow sweeps across the left side of the screen. (00:03:55)
Plot hole: Pike says he doesn't want women on his bridge, Number One being the one and only exception, and he keeps ordering Colt off it. His apology to Number One indicates that A) he doesn't think of her as female, and B) she's the only exception to his rule. So how does he overlook the very female crew-woman seated at the science station? (00:06:55)
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)
Revealing mistake: When the laser cannon starts firing at the Talosian rockface, a styrofoam block falls and rolls away on the left side of the screen. After a brief shot of the crew, we see the cannon still firing, and the exact same block falls and rolls off screen on the left again. (00:30:15)
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)
The Man Trap - S1-E2
Continuity mistake: Kirk jokes with Bones after they land about flowers and is holding some hay or grass in his hands. After Bones makes the comment about bribing girls, Kirk lowers his hand off screen but with the grass still in it. It jump cuts to a different angle from further away and suddenly his hand is empty, and there is no grass on the ground where he could have dropped it. (00:00:57)
The Man Trap - S1-E2
Continuity mistake: When Kirk is telling Crater that he needs him and his wife to stay on their ship till he finds out what killed his man, Kirk has his arms crossed. When Crater steps up to him and the angle changes, Kirk's arms are suddenly down at his side. This continuously changes back and forth between shots. (00:18:07)
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)
The Man Trap - S1-E2
Continuity mistake: When Rand brings Sulu the plate of food, it has a bowl of colored cubes on it. Then there's a cut to a close-up of Sulu eating the cubes when Green is staring at it, and the bowl is now a plate. Then in the long shot it's a bowl again. (00:24:22)
The Man Trap - S1-E2
Continuity mistake: When the creature makes it's way through the ship and finds McCoy's room, it stops near the wall with a red vent behind it. It changes back to Nancy in a dissolve cut, but suddenly it's much closer to the walk and is now closer to the vent, something that would not have happened by a simple morph like seen before. (00:28:45)
The Man Trap - S1-E2
Revealing mistake: In the corridor, as Sulu touches the face of the dead crewman, the man's eyelids flutter. (00:30:15)
The Man Trap - S1-E2
Revealing mistake: On the planet, as Kirk and Spock try to get to Professor Crater, Crater fires at and destroys the center support of the arch. As it settles, the parts are clearly hollow. (00:34:21)
The Man Trap - S1-E2
Audio problem: As Kirk low crawls behind some boulder and grass, his communicator flips open and closed. If it was opened, the sound of the channel opening should have been heard, but wasn't. (00:36:35)
The Man Trap - S1-E2
Other mistake: When Crater is hit by the phaser, his collapse is sped up. (00:36:50)
The Man Trap - S1-E2
Revealing mistake: Just after Kirk stuns Crater with his phaser, he gets up to get to Crater, when he does he bumps into a heavy stone monument,a prop that shakes visibly on contact. (00:36:58)
