The Man Trap - S1-E2
Revealing mistake: On the planet, as Kirk and Spock try to get to Professor Crater, Crater fires at and destroys the center support of the arch. As it settles, the parts are clearly hollow. (00:34:21)
Character mistake: In the scene when the shuttle is finally repaired and lifting off the planet, Spock asks "Fuel status?" and Scotty incorrectly answers "15 pounds PSI, sir. Approximately enough for one orbit." The correct answer would be simply "15 PSI" without the redundancy, as the P in PSI already signifies pounds. As an engineer Scotty would know this. (00:42:00)
Factual error: If this planet is a duplicate, an exact copy, of Earth, then Lake Okeechobee, the largest lake in Florida, is wrong. Seen from space, it is much larger and more distinct than the lake shown on this duplicate.
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.
Continuity mistake: Kirk has a sunburn on his face and chest (it appears to end partway down his chest-most noticeable in the scene shortly after his identity is revealed to the Klingons). First of all, how does one get a sunburn while flying through space (and one that does not match the pattern of the uniform). If one wants to explain it away as being from a recent Shore Leave or Enterprise tanning bed, the issue still remains that the intensity of the sunburn changes as the episode continues.
Deliberate mistake: When the Klingons post signs for their rules, they're printed in English. The Klingons have their own language, and people on Organia most certainly aren't English speakers. Even if the Universal Translator allows Kirk and Spock to hear in English, it wouldn't change the look of a sign.
Revealing mistake: Chekov covers Mara's mouth with his hand when he assaults her in the corridor. Kirk intervenes and throws Chekov against the opposite wall. Brown streaks form where Chekov's hands hit the wall, most likely from the brown makeup used to create Mara's skin tone. (00:32:20)
Revealing mistake: When Kirk and Garrovick are fighting at the end, Kirk knocks him down. As he helps him up, Garrovick leans against a huge boulder and the papier-mache rock moves very noticeably.
Character mistake: Spock expresses amazement that the natives of this planet speak Earth English, however, he and Kirk were both on the bridge when Uhura tapped into the planet's news broadcast and already know that they speak Earth English, and there's no reason to tell McCoy, because he heard it too. Commenting on it would be illogical. (00:07:00)
Space Seed - S1-E23
Revealing mistake: Just before Kirk and Khan fight in Engineering, Khan bends Kirk's phaser pistol in half, but the small hand phaser on top is still functional.
Revealing mistake: Just before Kirk finds himself in Trelane's "courtroom", look behind Kirk on the bridge above Spock's work station. The viewscreen with the planet on it is actually a piece of paper that's coming away from the wall.
The Ultimate Computer - S2-E24
Continuity mistake: The doctor and Spock are facing each other, the camera angle changes and they are suddenly shoulder to shoulder. (00:26:50)
The Alternative Factor - S1-E28
Continuity mistake: Lazarus had knocked out the transporter technician, but when Kirk arrives he is fine and operating the transporter. (00:37:35)
Shore Leave - S1-E16
Revealing mistake: During the scene with Sulu and the samurai, each actor casts three shadows. Plus as the samurai rushes Sulu, the "sky" appears black behind him.
Plot hole: How did the android Norman get aboard the enterprise? If he beamed aboard I'm sure someone would have noticed and where did he beam from? The Enterprise was nowhere near any planet and I'm sure they would have detected any spacecraft nearby.
Suggested correction: These are unanswered questions, not plot holes.
But something phrased as a question because it has no decent answer can constitute a plot hole.
The Man Trap - S1-E2
Plot hole: The salt creature needs salt, but there is no need for the creature to kill anybody, just have them deliver a large shipment of salt the next time some ship come to visit the planet.
Suggested correction: As shown several times, the creature is acting on craving and impulse. It's able to not attack Dr. Crater because they have a mutual relationship, as well as he provides salt for her from their supplies. But their supplies are running low, as he even stated they did have 25 pounds of salt but displays a jar with barely any left in it. It is reasonable to assume that he has had to start rationing the supply of salt to her to keep her till they could get another shipment. They were not getting the salt right off after Kirk arrived, and so the creature could not resist the urge to suck salt it needed out of the crewman when they were together alone, reason and logic being clouded by its desire and feral cravings.
Shore Leave - S1-E16
Character mistake: Yeoman Barrows is a crew member on an star ship and I assume has experienced or has trained to experience many different things she will encounter on the tour of duty but she freaks out and cries uncontrollably just because she sees Don Juan.
