Character mistake: Watkins is asked to check the bypass valve, there the woman appears, asked about the panel, it's obvious she's not part of the crew. Instead of calling security or Mr Scott he starts to describe the panel, which I'm assuming would be classified information.
Plot hole: If diverting the asteroid was so important, what was the crew doing on the planet to begin with?
Requiem for Methuselah - S3-E19
Factual error: Spock plays a piece on a harpsichord that he says is by Brahms, but Brahms was a late romantic composer and the piece is a simple baroque dance piece. Also by the time of Brahms the harpsichord was already obsolete, a composition like this wouldn't be sitting on a harpsichord.
Suggested correction: The first sentence is logical; if Spock is able to recognize the style as Brahms, then it should not possess the style and structure of Baroque music. The second sentence is not necessarily true because some romantic composers did write for the harpsichord. For instance, the late romantic composer Richard Strauss composed, "Divertimento for Chamber Orchestra after Keyboard Pieces by Couperin", which is scored with a harpsichord part.
Continuity mistake: In the opening, the crewman gets a few drops of the infectant on his hand, but the reddish mass on the wall remains. On the ship, when the spectral view is shown, the red mass is nowhere to be seen.
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.
Continuity mistake: When Sulu first emerges on the Bridge, Kirk confronts him, and standing a couple feet from the rapier. A second later, Kirk's a few inches from it.
Other mistake: In the Transporter room, as the Decontamination field is used, the shuttered lighting casts not only on Spock and Joe, but on the walls surrounding the chamber.
Factual error: In the opening sequence, Spock identifies the alien ship as possessing "ion propulsion" which he says is "unique technology." Scotty is similarly impressed and says, "They could teach us a thing or two!" Kirk later comments that "Advanced ion propulsion is beyond even our capabilities." However, even back in the 1960s, ion propulsion was physically feasible, while Warp propulsion was complete fantasy. Ion propulsion of any kind could never even reach lightspeed and would be incredibly primitive compared to Warp technology. In fact, we in the 21st Century have already developed ion propulsion, but it will probably take many hundreds or thousands of years to develop anything even close to Warp technology.
The Return of the Archons - S1-E22
Revealing mistake: The rocks pelting Kirk and the landing party when all hell breaks loose bounce when hitting the actors, the brick walls, and the concrete sidewalk.
Revealing mistake: In the Enterprise lab, as a sped up Spock goes to move away from McCoy and Chapel, McCoy's eyes follow his movements rather than looking at where Spock was supposed to be after he "disappeared."
Revealing mistake: As Kirk and company exit through the tunnel, the seams of the wall sections are visible.
Revealing mistake: As Trelane takes a swipe at Kirk, he hits a tree branch. As it breaks away, the building material it was made from is revealed, rather than it being wood.
Revealing mistake: In Trelane's castle, Kirk and Sulu are supposed to be frozen, but they slightly waver.
Continuity mistake: As there were two screen used models of the Enterprise, when the ship is seen flipping from one universe to the other and back, the nacelles of the Imperial Enterprise have the solid red fronts with what appear to be antennae.
The Man Trap - S1-E2
Revealing mistake: On the planet, as Kirk and Spock try to get to Professor Crater, Crater fires at and destroys the center support of the arch. As it settles, the parts are clearly hollow. (00:34:21)
Character mistake: In the scene when the shuttle is finally repaired and lifting off the planet, Spock asks "Fuel status?" and Scotty incorrectly answers "15 pounds PSI, sir. Approximately enough for one orbit." The correct answer would be simply "15 PSI" without the redundancy, as the P in PSI already signifies pounds. As an engineer Scotty would know this. (00:42:00)
Factual error: If this planet is a duplicate, an exact copy, of Earth, then Lake Okeechobee, the largest lake in Florida, is wrong. Seen from space, it is much larger and more distinct than the lake shown on this duplicate.
