Continuity mistake: When Losira comes for Kirk, he's holding Sulu's tricorder with both hands. When the angle changes to include her, he has it in one hand with his right hand at his side. Cut back to a three shot of Sulu, Kirk and McCoy, and Kirk has the tricorder in both hands again. (00:36:55)
Continuity mistake: After Marta's dance, Kirk and Spock are sitting an inch apart behind the table, then a foot apart, then an inch again and so forth every time the shot changes. (00:16:25)
Let That Be Your Last Battlefield - S3-E15
Continuity mistake: The planet Cheron is blue the first two times we see it on the view screen, but when the Enterprise enters orbit, and every time we see it thereafter, the planet has mysteriously turned red. (00:44:05 - 00:46:00)
The Empath - S3-E12
Continuity mistake: Gem's left hand is cupped around McCoy's right ear as she begins to heal him, but her hand keeps changing positions as the camera angles switch. (00:44:20)
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: When Kirk beams down to the planet, he selects the front transporter pad next to the steps, and closest to the door. When he materialises in the replica transporter room, he is on the same pad. When the scene cuts to a view of the empty transporter room, Kirk is no longer on the front pad. The scene cuts again, and Kirk steps off the front pad to walk to the control panel. (00:00:30 - 00:01:30)
Continuity mistake: When Scotty thwarts Garth, disguised as Kirk, attempts to beam to the Enterprise using the Queen-to-Queen level three code, Kirk throws a tantrum and accidentally loosens one of his controls during his rant right before he turns back to Garth.
Suggested correction: How is that a mistake?
Continuity mistake: After Spock nerve pinches Chekov when he goes mad and he is taken to Sickbay, the Tholian ship appears and hails the Enterprise. When Spock says "on main viewer," the shot of Loskene is on the screen, but the back of Chekov's head can be seen when it should be in Sickbay.
Continuity mistake: In the turbolift, Chekov is standing to the left, but when the door opens he has moved to the right and exits behind Spock. (00:10:40)
Continuity mistake: When Scotty, Kirk, and the others follow Spock's signal to the chamber with the Controller, they encounter Kara and she activates their pain bands. Spock's body has a pain band around his waist as the other men drop to the ground, but after McCoy tells Kirk, "Spock, no pain," the pain band is missing from Spock's body, then in the next shot it reappears when he goes after Kara's bracelet. (00:35:05)
Continuity mistake: When Kirk and his landing party beam down to the planet there are six shots of Morg, who have their right arms covered in fur in all those flipped shots, but when Morg attack the landing party it's their left arms covered in fur. Presumably, the first six shots were flipped for direction continuity. (00:13:15)
Continuity mistake: When Kirk and Mara are in the transporter room for intraship beaming, Kirk is wearing his usual Starfleet boots with heels, but while Kirk and Kang are fighting Kirk is wearing flat bottom boots. (00:43:25)
Continuity mistake: During the hand-to-hand fight scene, the stunt double playing Spock gets his hair mussed up, but immediately after the fight, Spock's hair is neatly combed and formed, as it was before the fight.
Continuity mistake: The first time we see the ship travelling at Warp Nine, it is moving in a level, straight path. Next time, the rear end is elevated above the line of flight. The next time, it's moving in level flight again.
Continuity mistake: As Kirk wipes a tear from Elaan's face, both cheeks are wet. A second later, both cheeks are dry.
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.
Continuity mistake: In the 40th Anniversary release of the complete original series, this episode opens with Scotty at the conn, making an extended log entry, wearing his third-season swept-back hairstyle, and it is very obvious that he is visually mouthing several completely different sentences than we hear in the audio. After the opening credits roll, we next see Scotty wearing his more typical relaxed hairstyle with slight bangs. It is apparent that, in remastering and editing this episode, they inserted footage of Scotty from another episode altogether. For whatever reason, it is a glaring mistake of both continuity and audio editing.
Continuity mistake: Just before Parmen starts mind-controlling Kirk, McCoy and Spock, he presents them with three gifts. Kirk receives a large, gold Greek shield, which the captain holds with both hands, in front of him, as the lengthy scene continues. In the wide shot, Kirk is holding the shield high up on his chest, completely obscuring his Federation insignia. In subsequent close-ups, Kirk is holding the shield down low, around waist-level, fully exposing his chest and insignia. Every time the camera cuts back to wide-shot, Kirk is again holding the shield up high on his chest.
And the Children Shall Lead - S3-E4
Continuity mistake: When Gorgon the Angel is on the bridge with the children, the positions of the children are different depending if the shot is from the rear of the children or the front.
The Enterprise Incident - S3-E2
Continuity mistake: When the guard opens the cell barrier, the light bars turn off, then slide back. As they come back out, they're already on, rather than the reverse of the opening procedure.