This Side of Paradise - S1-E25
Other mistake: As Spock and Kirk are fighting, Spock bends a steel bar with one of his blows. When he hits Kirk, though, it simply makes Kirk a little sore. A blow strong enough to bend a steel bar would shatter human bones.
Other mistake: Kirk and Spock stun two Klingon guards, yet despite being unconscious, the guard on the left jumps from the balcony and lands feet first on the ground. If he were really unconscious he would have simply tumbled down. (00:36:20)
Tomorrow is Yesterday - S1-E20
Other mistake: The Air Force police officer (played by Hal Lynch) was beamed up from inside the records room (after finding Kirk exiting the dark-room) but was returned outside the room... so he was physically transported INTO himself (as opposed to replacing the beamed-up future version at the exact moment and place he was removed as they did the pilot, Christopher).
Other mistake: Stiles gives a countdown for impact to Kirk saying "estimate it will overtake us in two minutes, sir." After only 31 seconds, Sulu starts his own countdown, saying "5, 4, 3, 2, 1, impact." Only 55 seconds have passed from the time Stiles started his countdown to actual impact. Everything was shot in real time without scene changes. Being off the impact estimate time by over a minute doesn't sit well considering a Starship's advanced sensors. (00:29:27)
The Man Trap - S1-E2
Other mistake: Sulu is asking Janice why people call inanimate objects "she"? Then gives an example. He says "Like, she's a fast ship." But the subtitles get this wrong and have him saying "Like, she's a bad ship". (00:23:30)
The Return of the Archons - S1-E22
Other mistake: After Sulu is "absorbed", he is beamed up to the ship. After materializing, his demeanor could be described as calm, gentle, meek and euphoric. After that scene, the captain's log quotes Kirk as saying "Mr. Sulu has returned, but in a highly agitated mental state." Was Kirk looking at a different Sulu than we were? A gentle, meek and euphoric condition incorrectly being touted as "highly agitated"? Time for Shore Leave. (00:01:28 - 00:03:53)
Other mistake: While on Starbase 11, Kirk and McCoy watch Pike on a starbase desktop monitor as his light keeps blinking no. When Kirk is with Mendez in his office discussing the Talos IV top secret file, Piper watches Pike on the desktop monitor in the office. Then Spock uses the monitor in his quarters to watch Kirk. All these monitors have the same dings and markings around their screens, which are also the same as other desktop monitors on Enterprise in the previous episode, The Corbomite Maneuver. (00:11:10)
The Corbomite Maneuver - S1-E11
Other mistake: When Kirk is in sickbay with McCoy he uses sickbay's desktop monitor to contact Spock on the bridge, then when Kirk is in his quarters he uses his own desktop monitor to contact Spock again. Both have the same paint dings and smudges around the console screens, revealing the same one was used during filming. (00:04:30 - 00:06:30)
Other mistake: When Kirk is lecturing Ayelborne in the council chamber, the actor behind him is mouthing Kirk's dialogue.
Other mistake: It's been established the planet is extremely dangerous to human life but when Jaeger, McCoy and DeSalle beam down they just have a simple mouth/nose mask on.
Other mistake: In the Transporter room, as the Decontamination field is used, the shuttered lighting casts not only on Spock and Joe, but on the walls surrounding the chamber.
Other mistake: In the opening, the planet looks to be turning the same as Earth does. On the viewer it is turning correctly. However, it is too quickly to be accurate, assuming it is a copy of Earth. If so, at this higher speed, the days would be shorter. Also, the ship should be moving at such a speed as to see the planet moving in the opposite direction.
The Man Trap - S1-E2
Other mistake: When Crater is hit by the phaser, his collapse is sped up. (00:36:50)