Continuity mistake: While Flavius guides Kirk, Spock, and McCoy to the city to find Merik, the foursome stop behind a group of trees. In the first wide shot, as Flavius explains they'll wait until dark, there are no red marks on the tree trunks, but in their closeups there are a few red marks (presumably from squibs), before the gunfire has even occurred. At the start of the second wide shot the tree trunks are still void of those marks, and when the police shoot at them that's when the red marks appear. (00:15:15)
Visible crew/equipment: After Kirk tells the policeman that he wants to see Merikus and "perhaps" he's a friend, the policemen lock the cell then leave, and when it cuts to a view of the cell from the side as Spock walks over to the steel bars, the overhead boom mic is visible inside the cell, over Spock. It's visible again, with a better view, when McCoy walks over to Spock beside the bars. (00:18:15)
Is There in Truth No Beauty? - S3-E5
Deliberate mistake: While Miranda is with Kollos, McCoy tells Kirk that he didn't reveal her secret because he respects her privacy, then when Miranda steps out of the room and concedes to obey, the next closeup of Kirk is a flipped shot. (00:34:05)
Shore Leave - S1-E16
Visible crew/equipment: While Kirk is with Spock, when Finnegan shows up again Jimmy boy gives in to the chase, then as Finnegan runs and shouts, "Here I am," the shadow of the camera equipment is visible at the bottom right side of the screen, as it follows Finnegan. (00:35:55)
The Gamesters of Triskelion - S2-E16
Other mistake: When Kirk agrees to fight in the arena at the end of the episode, he and the thralls are warned that touching an opponent's color will result in the loss of a weapon. Kirk does this several times during the fight, but isn't penalized in any way.
Continuity mistake: When McCoy places the old tricycle down on the ground, the handlebars are facing the right with its wheels facing the left. When McCoy is attacked by the diseased Only, Kirk and Spock subdue him, and as he lies on the ground the tricycle flips over between shots, so the handlebars suddenly end up facing the left. (00:04:30)
The Immunity Syndrome - S2-E18
Continuity mistake: When McCoy escorts Spock to the shuttlecraft hangar McCoy is wearing his short-sleeved medical tunic, but when Spock suggests that the doctor could wish him luck, in the next closeup McCoy is wearing his long-sleeved uniform. (00:29:40)
Continuity mistake: When Kirk's arrow hits Kras it protrudes from his leg, but in the next wideshot as Kras screams and stumbles the arrow is quite gone from his leg, but three shots later the arrow is back in his leg while he tries to pull it out. (00:43:40)
Visible crew/equipment: After Amanda tells McCoy about Spock's pet sehlat, when Sarek and Amanda walk away, the actors' multiple white tape marks are visible on the floor, under the table. (00:10:50)
Visible crew/equipment: At the hangar deck, after Kirk introduces Sarek to Spock and McCoy they all step forward, then as Sarek introduces his aides and his wife, the three white tape marks are visible on the floor behind them, where they had been standing. (00:02:15)
Character mistake: William Shatner mentions the sound enhancer is multiplied by 1 to the 4th. I think he meant 10 to the 4th.
Continuity mistake: After McCoy checks the Horta, he approaches Kirk with his tricorder in his left hand. The scene cuts to McCoy and Kirk and now McCoy's tricorder is in his right hand.
Continuity mistake: Spock and Kirk both arrive at the sizzling remains of a red shirt crewman, standing close together, but the next shot of the crewman's remains shows only one set of legs at the site (presumably Spock's), not two.
Revealing mistake: As Spock carries the crewman, the second spear hits a rock. As it does, you can see the Styrofoam chips fly up.
Factual error: The harpsichord Trelane plays is far too short and has pedals like a piano.
Revealing mistake: After being put in the cell, when the camera is in a closeup of Spock, you can see the lines in the prosthetic ears, and can easily tell where the makeup is blended into his real ear.
The City on the Edge of Forever - S1-E29
Continuity mistake: At the end, Kirk says "Let's get the hell out of here." Captain Kirk and 6 others were beamed up at the same time, but the Enterprise transporter only has 6 pads; presumably a red-uniformed crew member was lost in space.
Suggested correction: Short version is, the Enterprise has more than one transporter room. The Animated Series references at least four on the Enterprise from this era. There are also cargo transporters, which aren't normally calibrated for personnel, but can be, albeit at reduced capacity and increased energy usage. https://memory-alpha.fandom.com/wiki/Transporter_room.
The City on the Edge of Forever - S1-E29
Continuity mistake: In the beginning, the ship is shaken, and McCoy is injected with cordrazine, and falls down. As he lays, the hypo is lying under his body. After the cut, he's on his knees, holding the hypo.
Factual error: As Kirk, McKoy and Scottie age during the episode, their hair goes from brown to fully grey. Mr. Spock shows this to a lesser extent, but by the end of the episode, he has full streaks of grey. This isn't how grey hair works. It starts from the root and works it way outward over time to the end of the strand. Unless their hair is growing quite rapidly, and then cut to keep it short, they shouldn't have full heads of grey hair.
And the Children Shall Lead - S3-E4
Other mistake: At the end of the episode, Kirk commands the Enterprise to Star Base 4. Earlier in the episode, there was an unsuccessful attempt to beam up two crewmen left on the planet Triacus. They evidently remain there to this day.
