Continuity mistake: When "good" Kirk beams up from the planet, the insignia on his shirt is not there. Then it appears when he's walking with Scotty. (00:03:00 - 00:05:25)
Factual error: In the opening scene on the bridge, when Spock states the planet's properties, the circumference is given in US miles; the mass is given in metric tons; the density is given in metric grams per cubic centimeter; and the atmosphere is given as oxygen/nitrogen. No scientist of Spock’s standing would mix US and metric unit systems. The atmosphere composition should also be stated reversed as “nitrogen/oxygen” with the most abundant gas first. (00:42:00 - 00:59:00)
Suggested correction: That might only true in today's standards. But we have no idea what future generations will choose to make standard.
This is such a trivial criticism that it should be removed to be fair. Whatever measurement standard is used in the future, it will be uniform without mixing of different unit systems.
But that's an assumption based on what you think the future would be like. The British and Americans currently use a mix of different unit systems. While many US students use miles and pounds, they still calculate density as g/cm3.
Revealing mistake: A straight and level seam connecting the top and bottom halves of the tunnel Spock is crawling through is visible.
Suggested correction: Views of the tunnels made before the creature was wounded by Kirk and Spock appear almost perfectly smooth. It is explained that the creature exudes a powerful acid to dissolve the rock. This tunnel was made after the creature was wounded, so it is logical that the wounded portion of the creature would secrete less acid thus leaving an imperfection as the creature tunnels. This could be a case of incredible attention to detail by the set designer rather than an error revealed.
This correction is too much of a stretch to explain a perfect seam by the wounded Horta. Plus, if the Horta was secreting less corrosive substance, then that area would be less eroded, not more. If attention to detail was paid, then the area would have an outward seam, not an inward one.
Shore Leave - S1-E16
Revealing mistake: There is a wooden or straw hut - some kind of man-made structure - visible in the lower-left of the frame behind Kirk and Bones as they walk. (00:12:30)
Suggested correction: They're on a planet where their every thought can be almost instantly created in physical form. Within the context of the episode it wouldn't be unusual to see literally anything in the background. Perhaps one of them was thinking about something involving that structure and it was being constructed for them.
Character mistake: Kirk informs Spock via communicator the Horta is ten feet from him, and Spock insists Kirk kill it. First, both know they cannot kill it with their phasers, and second, Spock's demand for Kirk to kill the Horta runs counter to the Vulcan philosophy of respect for all life. Spock would never want to harm, let alone kill, another life form.
Suggested correction: At this point they don't have any proof that they can't kill it, and since Kirk is in danger, it's logical to try. Also, Spock is half human and he's concerned about his best friend being killed. Logical or not, he'll want Kirk to protect himself at all costs. Other episodes have shown where Spock doesn't always behave logically when his friends are at risk and he lets his emotions come out.
The City on the Edge of Forever - S1-E29
Continuity mistake: At the end, Kirk says "Let's get the hell out of here." Captain Kirk and 6 others were beamed up at the same time, but the Enterprise transporter only has 6 pads; presumably a red-uniformed crew member was lost in space.
Suggested correction: Short version is, the Enterprise has more than one transporter room. The Animated Series references at least four on the Enterprise from this era. There are also cargo transporters, which aren't normally calibrated for personnel, but can be, albeit at reduced capacity and increased energy usage. https://memory-alpha.fandom.com/wiki/Transporter_room.
Continuity mistake: When the "evil" Kirk appears, the Enterprise emblem is missing from his shirt. Then later, when he gets the brandy, the insignia is there. (00:04:45 - 00:06:20)
Suggested correction: When Kirk and Sulu are on the planet, they're shown not wearing the insignia. When "good" Kirk beams up, he too doesn't have the insignia. We just don't know where it came from, it could have been in their pocket.
The insignia is not removable, it's permanently attached. They wouldn't be able to remove it. The idea of a removable insignia wasn't introduced until STTNG.
While it might have been sewn on for production purposes, I saw this episode as indicating it was removable given the fact that they weren't wearing one on the planet. Plus, there have been other officers whose insignia is not sewn on in TOS.
This Side of Paradise - S1-E25
Continuity mistake: As Kirk sits on the deserted bridge, there is nothing out of the ordinary with him. After he sits at the helm position, the camera looks at him over the console, and there's suddenly a spore spewing plant to shoot him.
Suggested correction: The plant did not suddenly appear, it was there from earlier in the episode.
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.
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.
The Man Trap - S1-E2
Other mistake: When Crater is hit by the phaser, his collapse is sped up. (00:36:50)
Suggested correction: This wasn't a continuous shot though, we just don't know where they get the insignia, it could have been in his pocket. Both Kirk and Sulu are on the planet's surface without their insignia. And when "evil" Kirk beams up, he too doesn't have it on, even though later he does.
Bishop73
What possible reason could there be for the Enterprise Insignia, which is stitched to every uniform, to be in 'Evil' Kirk's pocket? No character has done this in any episode of Star Trek. They don't get them from anywhere, they are a part of their uniforms.