Deliberate mistake: At the very end, the Talosians send a final visual transmission of Vina and Christopher Pike, now whole and happy and reunited after 13 years, holding hands as they enter the Talosian elevator in the hillside. However, in this last shot, the elevator is still half-disintegrated, exactly as it was 13 years earlier when the Enterprise crew destroyed the hillside with a laser cannon. Within the context of "The Menagerie" storyline, this suggests that the Talosians never attempted to repair the elevator for 13 years (even though they continued using it). This incongruity is due to Gene Roddenberry cannibalizing his Star Trek pilot "The Cage," which contained zero footage of Jeffrey Hunter and Susan Oliver entering the intact elevator together (only the destroyed elevator). So, Roddenberry deliberately tried to "slip one by" the audience in this brief shot.
Suggested correction: There are reasons why the elevator would appear damaged. As the Talosians were in control of everything shown on the ship's viewer, the entire scene could be an illusion, or at least the elevator's condition may have been, with the Talosians choosing to allow the viewers to see the elevator in the same condition they last saw it. Just as likely, however, is that the Talosians truly never did reconstruct the elevator, as the whole point of their having a menagerie of other beings was an attempt to breed a race that could physically serve them, for their concentration on their mental powers had led to a complete inability and unwillingness to perform physical tasks (like repairing an elevator).
Still, as long as the Talosians are creating the illusion of Christopher Pike and Vina in their "restored" bodies, why not create an illusion of the elevator and hillside restored, as well? One big illusion of restoration, rather than a composite of dismal reality and happy-ending illusion? Again, to the point of my original post, the obvious incongruity is due to Roddenberry using the only happy-ending footage he possessed, that of Pike and Vina entering the half-obliterated elevator as they did at the end of "The Cage." Certainly, if Roddenberry only had the foresight to shoot Jeffrey Hunter and Susan Oliver entering the intact elevator, he would have used that footage instead. Any attempt to explain away the 13-year incongruity is mere wishful thinking.
This would qualify as a question, not a mistake. It is entirely plausible that the Talosians wouldn't bother to repair the elevator. It's also possible, as the previous correction points out, that the entire scene is an illusion. Remember, Captain Kirk sees Vina and Pike together on the planet literally moments after Spock wheels Pike out of the room. It's unlikely Pike had already been beamed down.
Revealing mistake: When the Talosians place Christopher Pike and Vina into the "picnic" illusion (in the countryside on Earth), Pike wanders around marveling at how real it all seems. Well, "real" except for the fact that Pike's body is casting 4 distinct shadows in 4 different directions on the ground, the result of studio set lighting.
The Gamesters of Triskelion - S2-E16
Revealing mistake: When the camera goes in on a close up of the phaser, when the trigger is pulled, the indicator light to signal a reaction by the intended target that's usually too small to be seen or hidden by animation is visible.
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.
Plot hole: 300 years is just too long for the children to be on their own. How did they keep their clothes relatively clean for 300 years? Since the kids are playing all day they aren't out in the fields planting and harvesting crops for food, how did they eat?
Suggested correction: For the clothes, it's highly unlikely that they wore the same sets for 300 years. They are in a town/city and on a world that is mostly empty of most human life now. They can easily just find more clothing their size from other houses and even stores. As far as food, children are very good scavengers.
The issue of clothing is not so much an issue as is the issue of food. Given that the children are growing at an incredibly slow rate, their metabolism is probably much, much, much slower and would require far less sustenance.
Character mistake: Kirk is surprised by Spock's behavior, but shouldn't everything about Spock be in his records? Kirk should therefore know about Spock's needs and have planned for them.
