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)
Visible crew/equipment: On the bridge, Uhura tells Kirk that Outpost 4 reported they're under attack, and after Scott says, "I've talked to my engine room, sir. We'll get more speed out of her," we can see the movement of the overhead boom pole's shadow as Kirk walks toward Uhura.
Continuity mistake: In Janice Rand's quarters, Charlie mentally throws Kirk and Spock against the wall. After they collide with it and slide down the face of the wall, there is a huge indention and crack where Spock hit. After a camera cut to Charlie, when the camera looks at Kirk and Spock again, there is no damage to the wall. (00:36:52)
The Immunity Syndrome - S2-E18
Character mistake: The officer at the helm is referred to as Lt. Kyle, and is named that way in the end credits. Yet throughout the episode, Captain Kirk keeps calling him "Kowel".
The City on the Edge of Forever - S1-E29
Continuity mistake: The bundle of clothes Kirk steals from the balcony changes several times while he and Spock face the policeman. The red shirt is not visible, then is hanging down on the right, then isn't. It then disappears from view until they reach Edith's basement, where Kirk puts it on. Two belts, two jackets and Spock's cap also seem to have added themselves to the bundle somehow. They're not there when Kirk first dismantles the tangle of clothes in the basement.
The Enterprise Incident - S3-E2
Audio problem: During the scene where Kirk is talking in the briefing room, the director was obviously not pleased with how James Doohan said his lines. Due to budget constraints, instead of re shooting the scene, they simply replaced Mr Scotts dialogue with another one. You can see it since at one point his lips are completely out of sync, even on the remastered edition. (00:06:40)
Operation -- Annihilate! - S1-E30
Revealing mistake: When Kirk and company beam down, the trees are brown. In the next shot, the trees are green. Most probably a different camera lens was used for the shots. (00:07:10)
The Return of the Archons - S1-E22
Continuity mistake: As Captain Kirk talks to Dr. McCoy, the background changes from stone to a red background in a closeup of Kirk's face. (00:27:05)
Other mistake: On some VHS editions of this episode, the back cover features a picture of what appears to be both good and evil Kirk sitting at a table, however this never happens anywhere in the episode. That picture is actually from the episode "What Are Little Girls Made Of?"
Continuity mistake: On Memory Alpha, the viewer beside the dead man in the purple jumpsuit keeps moving from his left side to his right and back again between shots. (00:09:10 - 00:10:10)
Continuity mistake: They said that engineering was "B" deck which is deck 2, but engineering is deck 7 which would be "G" deck.
Plot hole: The law officer who arrests Kirk recalls hearing Kirk call the "spirit" Bones. But he wasn't there when Kirk spoke to McCoy. He rushed into the scene several minutes later. If he's lying, how would he know that Kirk used the name Bones? He wasn't there to hear it. Even if he had been, Kirk did not refer to McCoy as Bones in that conversation. (00:10:50 - 00:19:50)
Continuity mistake: In a wide shot of the Capellons and the Klingon walking down the hill, the Klingon trips and falls to the ground and picks himself up. Next shot, tight group with Klingon, he is suddenly brushing off his pants.
Suggested correction: After Kras falls, the next shot you see him still on the ground and starting to stand up, although Maab blocks the view of him. The shot cuts to the rocks and then when it cuts back, you see Kras walk up and stand next to Maab, then he starts to dust himself off.
Suggested correction: Why would he not be doing that in the next shot? There is no continuity issue.
The City on the Edge of Forever - S1-E29
Character mistake: When Spock is finally able to determine that Edith must die to restore time, Kirk asks Spock how it will happen, and Spock tells him he can only estimate general events, not specifics. However, after Spock's previous attempt, he tells Kirk he'd seen her obituary. The obituary would necessarily include how and when she died.
Tomorrow is Yesterday - S1-E20
Plot hole: In the transporter room the captain calls to see if Major Christopher is ready, Christopher somehow knows exactly what button to press on the console to answer back.
Revealing mistake: As the Enterprise passes by the camera in the opening, as Kirk does the Log entry monologue, it's easy to tell where the studio lighting was positioned.
Revealing mistake: When Spock and "good" Kirk are searching engineering for the "bad" Kirk, there is an obvious cut in the shot just before "bad" Kirk jumps down from his hiding place.
Revealing mistake: When the "pleasant" Kirk and Spock go down to the engineering level to get the "animal" Kirk, they split up and "pleasant" Kirk meets the "animal" face to face. As he steps out from behind a screen type wall, you can see that the "animal" Kirk is really Shatner's stunt double helping to fill the double role. This can also be told by the size difference when the two are close together and the shot is from behind the double.
Other mistake: The action is shifting back and forth from the bridge where the alien ship is attacking and sickbay where McCoy is operating on Sarek. In two separate takes when the scene shifts to sickbay McCoy is standing at the operating table. I noticed a wisp of smoke rising from McCoy's right side (left side of screen). It appears to be from a cigarette in an ash tray below camera level either beside McCoy or near the head of Spock's bed.
Suggested correction: This was an intended physical effect to simulate the cryogenic surgery that McCoy was performing on Sarek.
The Enterprise Incident - S3-E2
Plot hole: Despite the Romulan ships keeping a close watch on the Enterprise, when they beam the disguised Cpt Kirk over to the Romulan vessel it goes undetected.