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.
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.
The Man Trap - S1-E2
Other mistake: When Crater is hit by the phaser, his collapse is sped up. (00:36:50)
