The Conscience of the King - S1-E14
Plot hole: After Kirk sees Leighton laying next to the rocks, he rushes over to examine him. He places one hand on Leighton's arm and the other on Leighton's waist and declares "It's Tom Leighton...he's dead." All this without the use of a medical tricorder or even the experienced opinion of the ship's doctor to confirm what Kirk is seeing. (00:10:46)
The Empath - S3-E12
Plot hole: Spock calculates that it will take 72 hours for the solar flare to pass, and Kirk orders the Enterprise out of the area. 3 days is a long time to go without food or water, and as the station is deserted as far as they know, there'd be no way to supply themselves, but the Enterprise leaves without a second thought.
Plot hole: Commodore Decker takes over command of the enterprise but Spock says if McCoy can certify him incompetent (which he obviously is) he can be relieved of command. McCoy says he will certify him now, so why doesn't he? In other episodes it has been stated that McCoy can order anybody regardless of rank to an examination to see if they are physically or mentally fit.
Plot hole: If diverting the asteroid was so important, what was the crew doing on the planet to begin with?
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.
