Continuity mistake: When Kirk, Bones and Spock are commanded to stop, and raise their hands, they do so. After a moment, Kirk starts to lower his hands. After the camera cuts to a shot from behind, Kirk's hands are by his sides and he goes for his phaser. After another warning shot, he says "I think he means it." The camera goes back to facing them, and his hands are up again.
Revealing mistake: After Kirk and party are captured by the police, a montage of scenes depicting the planet's buildings plays while the log entry is heard. One of the buildings shown, though hard to read, has the title "Massachusetts Institute of Technology" (M.I.T.) above the columns.
Revealing mistake: During the televised fight, in the wide angle shots, you can tell it's Spock's stunt double fighting.
Continuity mistake: The chain symbol on Kirk's shirt goes from dark to light and back several times.
Revealing mistake: Kirk uses a sword to cleave a Roman guard during his escape from the TV studio, but there is no blood on it. Later, though, when Claudius stabs Merrick in the back, there is blood on the knife blade.
Revealing mistake: Kirk uses a submachine-gun to shoot the lock of the cell holding Spock and McCoy, but no bullet holes appear, nor is the lock damaged.
Revealing mistake: A Roman guard empties half a magazine of bullets from his submachine-gun into Flavius, but there are no bullet holes in his body, nor blood on the floor from the wounds inflicted by the bullets.
Visible crew/equipment: Set lights are reflected in Spock's tricorder screen before he closes the cover.
Continuity mistake: Kirk is talking to Scotty on his monitor, after they have finished talking Kirk goes to switch off the monitor by pressing the button just below it. If you watch very closely you will notice Mr Scotts image fades from the screen before Kirk even touches the button. (00:07:05)
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)
Continuity mistake: Gary Seven is talking to his computer, we then switch to Kirk and Co and after a few moments with them we cut back to Gary Seven. Somehow in that time, while talking to his computer he changed his clothes. (00:13:40)
Continuity mistake: After Gary turns on the typewriter and tells Roberta to give her report but not with her fingers, she responds, "Well, how do you expect me to type, with my nose?" But the typewriter types, "How do you expect me to type, with my nose?" omitting the "Well." It didn't edit her question, because we see from the rest of the scene that it types absolutely every word she says until Gary turns it off. (00:17:45)
Continuity mistake: When Isis meows and enters the inner office, the door is open several inches and the lights inside the room are on. When Gary Seven follows her in a few moments later, the door has nearly closed itself and the lights inside are off. (00:20:25)
Plot hole: Scotty is receiving images of the launch, supposedly from an orbiting satellite. But many of the camera views are obviously from ground level, and couldn't possibly have been taken from orbit. It's not a rebroadcast from a ground camera, either. The implication is clearly that Scotty is is picking up a live satellite feed. (00:34:30)
Revealing mistake: After Scotty finally locates Seven on the gantry while he's tampering with the rocket, it cuts to a quick shot of Kirk and Spock, then in the following shot of Roberta when she turns the vault's combination locks, the stunt wire is visible behind her as it moves up to turn the door's wheel handle. (00:35:25)
Continuity mistake: Isis is an all-black cat, but in a few shots, her "stunt double" with white paws can be spotted. The cat lying on the floor of the transporter room when Gary Seven beams aboard is a white-pawed double.
Continuity mistake: As Gary Seven beams in, Scotty's hair changes between shots.
Plot hole: Spock claims that history is unchanged at the end of the episode according to the library tapes - how would he know? If history changed, the tapes would change too. And unlike in "City on the Edge of Forever", there's no Guardian around to keep people from being influenced by an altered timeline.
Continuity mistake: Gary Seven pushes a pen holder over to open the doors. The pen wasn't returned to the upright position, but was up when Kirk came in.
Continuity mistake: When the computer opens and begins operation in Gary Seven's office, it's white. In the close up, it goes from white to purple when asking for identification. Afterwards, the color continues to change.
Chosen answer: If they're in orbit, they're being pulled along by the planet's gravity well, therefore, impulse engines would only be used for minor corrections and would be "on standby" while in orbit, but not active. (Like keeping your car idling without revving the engine and creating plumes of exhaust).
Captain Defenestrator
Thank you for the info.
Movie Nut