Continuity mistake: When "good" Kirk beams up from the planet, the insignia on his shirt is not there. Then it appears when he's walking with Scotty. (00:03:00 - 00:05:25)
Continuity mistake: All during the episode there are scratches on the left cheek of the "evil" Kirk. When the "Good" Kirk and the evil Kirk confront each other on the bridge, there's a shot where the scratches are on the right cheek of the evil Kirk.
Other mistake: Spock records a log entry as the "second officer". It appears they got "first officer" confused with "second in command." (00:36:15)
Plot hole: Because of the magnetic ore on the work clothes of the man who beamed up, the transporter made duplicates of everything put through it, and so couldn't be used. This was further complicated by the control and power circuits being blasted by the "evil" Kirk. However, the ship carries a number of shuttle craft, which no-one mentions.
Continuity mistake: When the "evil" Kirk appears, the Enterprise emblem is missing from his shirt. Then later, when he gets the brandy, the insignia is there. (00:04:45 - 00:06:20)
Suggested correction: When Kirk and Sulu are on the planet, they're shown not wearing the insignia. When "good" Kirk beams up, he too doesn't have the insignia. We just don't know where it came from, it could have been in their pocket.
The insignia is not removable, it's permanently attached. They wouldn't be able to remove it. The idea of a removable insignia wasn't introduced until STTNG.
While it might have been sewn on for production purposes, I saw this episode as indicating it was removable given the fact that they weren't wearing one on the planet. Plus, there have been other officers whose insignia is not sewn on in TOS.
Visible crew/equipment: In Kirk's quarters, as the camera goes to a close up on the "evil" Kirk, watch the reflective strip behind him. The movements of the camera are reflected and noticeable.
Other mistake: On some VHS editions of this episode, the back cover features a picture of what appears to be both good and evil Kirk sitting at a table, however this never happens anywhere in the episode. That picture is actually from the episode "What Are Little Girls Made Of?"
Revealing mistake: As the Enterprise passes by the camera in the opening, as Kirk does the Log entry monologue, it's easy to tell where the studio lighting was positioned.
Revealing mistake: When Spock and "good" Kirk are searching engineering for the "bad" Kirk, there is an obvious cut in the shot just before "bad" Kirk jumps down from his hiding place.
Revealing mistake: When the "pleasant" Kirk and Spock go down to the engineering level to get the "animal" Kirk, they split up and "pleasant" Kirk meets the "animal" face to face. As he steps out from behind a screen type wall, you can see that the "animal" Kirk is really Shatner's stunt double helping to fill the double role. This can also be told by the size difference when the two are close together and the shot is from behind the double.
Suggested correction: This wasn't a continuous shot though, we just don't know where they get the insignia, it could have been in his pocket. Both Kirk and Sulu are on the planet's surface without their insignia. And when "evil" Kirk beams up, he too doesn't have it on, even though later he does.
Bishop73
What possible reason could there be for the Enterprise Insignia, which is stitched to every uniform, to be in 'Evil' Kirk's pocket? No character has done this in any episode of Star Trek. They don't get them from anywhere, they are a part of their uniforms.