During the showdown between Good Kirk and Evil Kirk on the bridge, Evil Kirk's scratch marks are suddenly shown on the right cheek instead of the left as they had been throughout the episode.
This episode begins with the Captain down on the planet's surface wearing a gold shirt with no insignia. When he beams up to the Enterprise, he is still wearing a gold shirt with no insignia, and his "evil half" also transports in wearing the same: a gold shirt without any insignia. Scotty offers to walk the Captain to his quarters and, miraculously, when we cut to the Captain and Scotty in the corridor, the Captain's shirt has sprouted an insignia as has the evil twin's shirt when he walks into Dr. McCoy's medical bay.
There are 5 Captain's Log entries. Kirk makes the first 4 entries on the following Star Dates: 1672.1, 1672.9, a supplemental entry at 1673.1, and 1673.5. The last Log entry is then made by Spock at 1673.1 again, showing that his log entry should have occurred at approximately the same time as the supplemental entry, rather than after Kirk's last entry.
Evil Kirk's phaser changes between cuts in the shoot-out in Engineering.
After Good Kirk says "If I'm to be the captain, I have to act like one," he and Spock separate. After Spock walks off-camera, there is a splice (slight frame jerk in what is supposed to be a continuous, stationary shot) before Evil Kirk lowers himself down to floor level.
(at around 25 mins) The split-screen becomes obvious when the evil Kirk is lying on the floor: two sets of knees can be seen where the seam is.
When Sulu, stuck on Alpha 177, comments on his communicator about "the skiing season opening down here" to Good Kirk in the briefing room, Spock enters, sits at the computer console and interrupts their discussion, pressing his communicator button on his console. The communication console's white "in use" light does not illuminate, yet Spock clearly makes contact with Sulu.
The first few shots of this episode are reversed for an unknown reason.
During the confrontation in engineering the Kirk facing away is taller than the one facing the camera.
Sulu and his landing party are subjected to freezing temperatures, at one point as low as -117 degrees, yet we can't see their breath.
Shortly after 22 min, Kirk and Spock enter "the lower levels, the engineering deck" to apprehend the impostor Kirk. They face a "whoosh" door while setting their weapons to "base cycle to stun, not to kill". They walk forward and enter the chamber in front of them as seen in the following shot, but no characteristic "whoosh" sound is heard to signify a door opening.
There is a nearly 6-second interval of suspenseful silence after the "2 halves" of the alien dog are transported away, then over a rear shot of Spock's head turned to the left, the sound of the transporter operating - "automatically" since there is no sound of its controls being operated first - starts just over 1 second before Spock gives the order to "Reverse!"
When Good Kirk is releasing Evil Kirk from the restraints in sick bay, Evil Kirk's head is turned away from the camera, but his jaw can be seen moving as if he is saying something, yet no audio is heard.
In addition to the largest problems noted, mainly with why they just do not use a shuttlecraft to rescue the landing party, it is explained that they tried to beam down thermal heating units, but they failed to operate because they were duplicated as well. They could have beamed down a few dozen or so blankets? If those are duplicated, then at least the landing party would have more to use.
There appears to be no in-universe explanation of why no transporter engineer was required to work the controls to beam up "evil Kirk". The transporter room was empty, so the transporter initiated and completed the beam up all on its own.
If Kirk had drunk nearly a whole bottle of Saurian Brandy, a simple alcohol test would also have proved that it was not Good Kirk that attacked Janice. This is a fairly obvious oversight.
While the Enterprise does house a fleet of shuttlecraft (four in all), this feature of the ship had not yet been introduced in the series. Hence, the reason they are not suggested to retrieve Sulu's endangered away-team. When shuttles were introduced later in the season, this seemingly presents a plot hole, yet this can be easily explained. At the time of Sulu's emergency, in that the shuttlebay may have been damaged in some off-screen event, or that all of the shuttles were out of service, due to damage or maintenance. (It is, however, unlikely that all four shuttlecraft was out for maintenance at the same time.)
Spock states that the thermal heaters beamed down to the stranded landing party duplicated and wouldn't operate. Since the transporter splits objects and people into two opposite parts there should've been two of every heater they beamed down. So, there would be a functional and non-functional one. They could have beamed down non-functioning heaters and the duplicates would work.
Spock erroneously refers to himself as "second officer". His title is "first officer" or "second-in-command".
Spock's speech and mannerisms betray much emotion throughout this one. Apparently Leonard Nimoy had not yet perfected his way of performing the character.
When McCoy speaks of Kirk's two halves, Spock points out that he himself has two halves. He refers to them as a "human half," and an "alien half." Spock would never refer to his VULCAN half that way. If anything, he would consider the human half to be the "alien" half.
When McCoy orders the necropsy, he hands the dog's remains off to a technician in ship's services red, not sciences blue.