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.
Character mistake: Spock says that Vanderberg said there were thousands of these silicon nodules, but Vanderberg actually said there were millions of them. Not a mistake Spock would make.
Character mistake: When Spock and Kirk pursue the Horta, they come to a fork in the tunnel. Kirk points right and tells Spock to go left. Then he points left and says he'll go right.
Continuity mistake: After his initial mind meld with the horta, Spock tells Kirk, "That's all I got, Captain: waves and waves of searing pain." A minute later, he says that it's "a highly intelligent, extremely sophisticated animal" that calls itself a horta. Apparently, waves of searing pain were not all that he got after all. Unlike Spock to be so imprecise.
Plot hole: Spock has absolutely no way to know, yet, that the horta only secretes her corrosive substance when tunneling: he hasn't had time to examine her or to do more than determine that she does indeed secrete a substance that cuts the tunnels. So he should at the very least scan the piece of her that falls off before he picks it up with his bare hands. Major lapse of logic, which given his character goes beyond a character mistake.
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.
Continuity mistake: After McCoy checks the Horta, he approaches Kirk with his tricorder in his left hand. The scene cuts to McCoy and Kirk and now McCoy's tricorder is in his right hand.
Continuity mistake: Spock and Kirk both arrive at the sizzling remains of a red shirt crewman, standing close together, but the next shot of the crewman's remains shows only one set of legs at the site (presumably Spock's), not two.
Continuity mistake: As Kirk is crawling through the tunnel leading to the Horta's nest, a tight view from his left side shows light shining on his face and darkness behind him. When the shot changes, though, to the view from the nest, there is light behind him and darkness on his face.
Other mistake: Kirk and Spock stun two Klingon guards, yet despite being unconscious, the guard on the left jumps from the balcony and lands feet first on the ground. If he were really unconscious he would have simply tumbled down. (00:36:20)
Continuity mistake: The Organians cause all the weapons to overheat, and everyone drops them to the floor. When Kor moves to the desk to call his ship, though, he's wearing his disruptor. It's gone again when he returns. (00:41:45)
Visible crew/equipment: After the Klingon vessel's attack on the Enterprise, while returning fire just as Kirk orders to maintain firing range at 100% dispersal pattern, the set's unfinished wood plank with grey paint drip marks can be seen at the bottom of the screen. Additionally, at the end when Spock goes to stand beside Kirk's chair (also when he walks away) the actor's mark can be seen on the floor by Spock's feet.
Visible crew/equipment: When Kirk is thrown into jail with Spock you can see the movement of the entire blue crash mat used to break his fall.
Continuity mistake: When Kirk orders the crew to fire phasers; the exterior shots show the ship firing torpedoes, and torpedo explosions flashing out in space.
Factual error: When Kirk/Spock enter/leave the Council Chamber, the doors quietly open unaided (as though there were motion detectors in operation), yet the Organian culture - determined by Spock to be approximately Class D minus on Richter Scale of Cultures - would not have had such technology. A fact overlooked by Kirk and more importantly, Spock.
Character mistake: When Kor describes the effects of the mind-sifter to Kirk (who is still in disguise as an Organian), he says the machine would leave him "more vegetable than human." There is no reason a Klingon would reference humans while speaking to a person he believed to be Organian.
Other mistake: When Kirk is lecturing Ayelborne in the council chamber, the actor behind him is mouthing Kirk's dialogue.
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.
The Alternative Factor - S1-E28
Continuity mistake: Both the positive and negative versions of Lazarus have a long mustache and a fairly full "waterfall" beard - until the scene in the briefing room, when inexplicably, the mustache and beard are both suddenly so thin they're barely visible. As soon as they beam down to the planet, however, the much thicker facial hair is restored. (00:23:00 - 00:24:30)
