Deliberate mistake: So that he can look in the right direction, toward Lincoln, a shot of Kirk is reversed before the first battle, putting his uniform insignia on the wrong side. (00:25:45)
Revealing mistake: When the Enterprise is attacked in the prologue, some of the crew grab onto the central console (that Sulu and Chekov usually sit at). The console noticeably lifts up from the stage surface, almost falling over. Twice.
Is There in Truth No Beauty? - S3-E5
Visible crew/equipment: When Kirk turns to follow Miranda across the arboretum, the camera shadow is briefly visible on the wall at the lower left of the screen. (00:29:50)
Revealing mistake: In the middle of the episode Spock goes to Plack Tao to meditate. We see a shot of him and then we see some other people. At this moment look directly behind all of them and you will see Spock waiting for his next shot.
Is There in Truth No Beauty? - S3-E5
Factual error: The Enterprise accidentally travels a short distance outside the galaxy and can't find its way back. But they'd have to travel for months to get so far outside the Milky Way that they couldn't, well, just turn around in the void and see it. Our galaxy is huge. 100,000 light years across. Very huge. And that barrier may surround the galaxy, but even it is big, pink and visible.
Revealing mistake: "Trek's" new 3rd season uniforms were tighter-fitting than their velour predecessors, presenting a problem for some actors. When the landing party beams down in this episode, the outline of William Shatner's tummy-wrapping girdle is very visibly showing through his costume. (00:13:10)
Revealing mistake: Isis the cat was disinclined to hold still for special effects shots. When Gary Seven beams off the Enterprise with the cat in his arms, the position of her head jumps several inches as they're dematerializing. (00:10:10)
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)
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)
Revealing mistake: During the Court Martial scene, a directorial error led to Kirk's exit from the briefing room in the wrong direction. He walks off screen into what would have been a solid wall or corner. The briefing room's only door is on the other side of the room. (00:39:15)
The Empath - S3-E12
Continuity mistake: During Kirk's torture scenes, the back shots have Kirk's arms stretched wide apart and yanked straight - the front shots have the chains going overhead and his arms are bent at the elbows.
Is There in Truth No Beauty? - S3-E5
Continuity mistake: At the dinner for Miranda, Kirk drains his glass. No one refills it, but it's nearly full again a few shots later. (00:08:25 - 00:10:35)
Suggested correction: Kirk's glass is not empty at 8:25, it is the top of the decanter in front of his chest that looks like an empty glass in the shot. Later Kirk empties his glass during toasts and refills his own glass as he watches Marvik leave the room.
Continuity mistake: When Chekov sits outside the general store chatting with Sylvia, his left arm and her right alternate from entwined to un-entwined and back again as the shots change. (00:27:40)
Who Mourns for Adonais? - S2-E2
Continuity mistake: Kyle reports the landing party's whereabouts on the surface, and Spock asks, "And Apollo?" Kirk had no chance to call the ship after Apollo revealed his name - so Spock should not have known it. (00:22:10)
Continuity mistake: After Garth attempts to convince Mr Scott that he is Captain Kirk and to beam him up, while he is banging his fists on the floor in anger he transforms back into himself and the fly like ring on his finger breaks and slides out of shot. It's quite hard to see but it does. The next time we see Garth's hand his ring is intact yet he has not transformed himself again to repair it.
Continuity mistake: When the prosecutor visits the cell, Kirk's hands on the bars change positions when the camera angle reverses. From the inside, there's one bar between Kirk's hands. From outside, there are two. (00:28:10)
Continuity mistake: When the giant cat breaks down the cell door, Korob falls beneath it face down with his head toward the door. In the very next shot, he's in a completely different position - face up with his feet toward the door. (00:43:30)
Other mistake: Kirk's voice-over log entry says he's been "placed on the surface of an asteroid." The Metrons earlier referred to it as a planet prepared for them with a suitable atmosphere. How and why does Kirk suddenly assume that it's an asteroid rather than a full sized planet? As an experienced space veteran, Kirk, who has already been told that it's a planet, would never make such a mistake. (00:23:45)
Other mistake: Scotty has a science patch on instead of the engineering patch in this episode.