Why don't they just beam up the landing party and have a security team standing by to subdue the "evil" versions when they come through? It would buy time to find a solution, and even if no solution is found, wouldn't dying as split good and evil parts be preferable to freezing to death?
When "evil" Kirk blasts the panel in Engineering, why do Spock and "good" Kirk not report it to a repair crew, but instead, have Scotty stumble on to it later?
When "good" Kirk and Spock step into the transporter to go to sick bay, there is slight jump in the frame before "evil" Kirk's blood-stained hand thrusts onto the screen - revealing the cut that allows William Shatner to be in two places at once.
Apparently, the transporter isn't just giving Kirk split-personality problems; when Spock goes to reunite Kirk's two halves, watch him as he engages the beam and you will see his head and upper body vibrating, as though he were going to split in two.
When beamed up (and before on the planet) the Kirks had no chest insignia on their uniforms, yet as they both started to wander the ship, the insignia was present on both with no time for either to have got changed. Indeed, the first place good Kirk goes is to his quarters at which point he changes into the green uniform, but this was after the insignia had appeared.
On the bridge, Navigator Farrell's uniform goes from bearing the Enterprise chest insignia when Spock leaves, to having none when evil Kirk arrives, yet in that same scene, the insignia is present again when Farrell turns around to face evil Kirk.
When the evil Kirk makes the good Kirk drop his phaser during their fight, it falls behind evil Kirk. He then just bends down and picks it up, without having to back up or turn around to find it.
Evil Kirk does such a good job with the makeup that Rand's fingernail marks are completely invisible to Wilson (and the audience) when he knocks him out and takes his phaser. Yet in the next scene in the engine room, we see one of them on his cheek. Either it's some really fast-decomposing make-up or Evil Kirk wiped it off to show that one mark.
After trapping "evil" Kirk on the bridge, Shatner's double's hair is darker with obvious amounts of gray.
In sickbay after Spock and the Good Kirk subdue the Evil Kirk, the status monitor for the Evil Kirk's bed isn't on, even though McCoy has said he's too weak to give a tranquilizer to and will be waking up soon.
When Kirk confronts the evil Kirk on the bridge, the viewscreen is off in one scene and then on again in another and then off again.
Despite various novels, fan speculation, and official and unofficial Enterprise blueprints, it seems clear in this episode that the Enterprise only has one six-person "standard" transporter - if it goes out, they've got nothing else to beam people with. There's no indication the malfunction here would somehow "contaminate" any other transporters - and it'd be pretty stupid design to make them that way anyway.
Scotty tells Wilson to get a synchronic meter to check the transporter after he beams a contaminated Fisher aboard. Then Wilson goes off without double-checking and Scotty beams Kirk on-board.
Rand and Spock seem wildly out of character at the end of the episode. She's all but raped by the evil Kirk, and Spock leers at her and comments that he had "interesting qualities."
Spock refers to his human half and his "alien half," and says the alien half is submerged. Not only does he typically act and consider himself a Vulcan, but he hardly keeps his Vulcan half "submerged."
So Kirk keeps make-up in his cabin?
When the evil Kirk knocks out the good one and goes to the bridge, Farrell clearly says, "No word from Mr. Solo, sir."
Sulu fires his phaser at a rock to heat it up - he holds his hand still but the beam moves widely back and forth over the rock.
The heart monitor on the sickbay bed that evil Kirk is on makes a thumping noise even after he gets off of it. It speeds up as he gets into his fight with good Kirk, but he's nowhere near it.
In the opening scene with Kirk and Sulu, the film is spliced in backward - their hair is parted on the wrong side. Also no one in the landing party has insignia. Presumably the director "flipped" the camera and tried to cover. (This is fixed in the DVD and remastered versions.)
The phaser in evil Kirk's hand in Engineering switches between a smaller Type 1 in the long shots, but a larger pistol-type Type 2 in the close-ups.
When McCoy asks how Kirk feels at the end, Shatner turns and then stops to answer him. Then the camera cuts to a close-up of Shatner and he turns again to face McCoy.
Sulu asks them to beam down some hot coffee twice. Why didn't they? It would have been duplicated, but would that not be a good thing in this case? They could have also beamed down heavy outer clothing, blankets, and shelters.
Spock records a log entry as the "second officer". It appears they got "first officer" confused with "second in command".
Why didn't they send a shuttlecraft to pick up the freezing officers on the planet?
Yeoman Rand scratches the left side of the "evil" Kirk's face. In the final confrontation between the two Kirks on the bridge, the scratches have switched to the right side of "evil" Kirk's face.
Janice Rand: (startled) Oh! Captain. You startled me. Is there something that you... can I help you, Captain?
Animal Kirk: "Jim" will do here, Janice.
Kirk: (his two halves reunited) Thank you, Mr. Spock - from both of us.
Sulu: (freezing on the planet's surface) Any chance you can lower us down a pot of hot coffee?
Kirk: I'll see what I can do.
Sulu: Rice wine will do if you're short on coffee.
Spock: (speaking softly to Yeoman Rand) The impostor had some rather interesting qualities. Wouldn't you say, Yeoman?
Spock: If I seem insensitive to what you're going through Captain, understand--it's the way I am.
McCoy: You have a point, Spock?
Spock: Yes. Always, Doctor.
Spock: (to Captain Kirk) You're the captain of this ship. You haven't the right to be vulnerable in the eyes of the crew. You can't afford the luxury of being anything less than perfect. If you do, they lose faith and you lose command.
Kirk: I have to take him back inside myself. I can't survive without him. I don't want to take him back. He's like an animal. a thoughtless, brutal animal. And yet it's me. Me!
McCoy: We all have our darker side. We need it; it's half of what we are. It's not really ugly, it's human.
Spock: You have here an unusual opportunity to appraise the human mind, or to examine, in Earth terms, the roles of good and evil in a man. His negative side, which you call hostility, lust, violence; and his positive side, which Earth people express as compassion, love, tenderness. And what is it that makes one man an exceptional leader? We see here indications that it is his negative side which makes him strong -- that his evil side, if you will, properly controlled and disciplined, is vital to his strength. Your negative side, removed from you, the power of command begins to elude you.
Kirk: You're too beautiful to ignore. Too much woman.
The original script called for Spock to "karate" chop the evil Kirk at one point. Leonard Nimoy felt the action was too violent for a pacifist character, and so developed the famous "Vulcan Nerve Pinch" instead.
This was originally scheduled to be the fourth episode.
This episode marked the first appearance of Kirk's alternate green uniform. It was introduced primarily to tell the "good" Kirk from the "evil" Kirk. However, the producers liked the idea of setting the captain apart with a different colored uniform so they used it frequently throughout the series.