Revealing mistake: When Kirk & Spock beam down with Lincoln to the supposedly newly-created non-volcanic landscape, there are footprints all over the ground. They disappear a few shots later, though.
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.
Revealing mistake: When Abraham Lincoln shoves the Klingon away from him during their fight, the Klingon collides with a heavy boulder which moves several inches at impact.
Revealing mistake: About 4/5 through the show, while the Vulcan is being killed, if you look at Lincoln's wrist, you can see his makeup line.
Continuity mistake: In Kirk's log entry, which he somehow makes from jail without a tricorder, he states that 5 witnesses heard him speak to the "spirits." This isn't true, and Kirk ought to know it. The crowd rushed in through an archway after he spoke to Spock and McCoy, and they were all too far away before to hear him. (00:10:50 - 00:26:00)
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: 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)
Revealing mistake: Zarabeth tells Spock that Zor Khan only left her what was necessary to survive in the ice age. Mascara, eyeliner, lipstick and hairspray were apparently considered survival necessities. Yes, we know the actress "had" to wear make-up. But in a prehistoric setting, it shouldn't look as though she did. She could and should have been given a more "natural" make-up job - and an unlacquered hairdo. (00:38:25)
Audio problem: In Zarabeth's cave, when McCoy says, "You've been dishonest with me, Spock," his lips are completely out of sync with his words. (00:42:00)
Character mistake: Spock tells Zarabeth he came from a world "millions of light-years away." The galaxy is only about 100,000 light-years across - the area the Federation has explored even smaller.
Other mistake: The time that Kirk winds up in doesn't look anything like the what he was viewing on the disk.
Suggested correction: The entire planet isn't going to look exactly like what he saw on the disk. The disk will show random scenes to give the viewer an idea, but we can't expect the whole planet to match that image.
Visible crew/equipment: The shadow of a boom mic is seen against the rock walls of the cave follows Spock and McCoy when Spock pulls McCoy off Zarabeth.
Other mistake: As Kirk nears the portal, the edge shimmers just before he gets to it. As he goes through it, his actions are greatly slowed rather than natural.
Continuity mistake: After Kirk knocks the jailer out, there's a bit of stew on the cell's door above the lock. After Kirk drags the man into the cell and closes the door, the bar above the lock is clean and dry.
Revealing mistake: For the final time in "Star Trek's" 3-season run, Chekov mysteriously vanishes from the bridge to be replaced by that tall blond doppelganger, thanks to an old piece of 1st season stock footage used for the special effects insertion of the view screen. The costumes are also noticeably different from 3rd season's uniforms. (00:14:05)
Continuity mistake: Lt. Galloway, who was killed off the season before in "The Omega Glory," is resurrected without explanation for this final episode. (00:24:25)
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)
Continuity mistake: During Spock's Court Martial, Chekov says that General Order 4 is the only exception to Starfleet's no-death-penalty policy, and Sulu and the others agree. However, according to "The Menagerie," that exception is General Order 7, not 4.
