Space Seed - S1-E23
Corrected entry: During Kirk's fight with Khan in engineering, he pulls a white rod from a console and uses it to subdue Khan. The rod is very light, and several times when Kirk hits Khan with it, Khan shows no reaction at all.
Requiem for Methuselah - S3-E19
Corrected entry: Mr. Flint grabs the Enterprise out of orbit and transfers it onto the table. We assume, because the ship is small, it doesn't weigh much. However, Star Trek canon states the Enterprise weighs 190,000 metric tons, size not withstanding. There's no way that small table could hold such a massive weight.
Correction: We have no idea of how the technology he uses works. If he can shrink the ships down to a miniature size and instantly put everyone in suspended animation, there's no telling if he can alter the weight as well. Not to mention the fact that if he has such advanced technology, he could have a table that's able to bear the weight.
The old "Fantastic Voyage" problem. There are only 2 ways to make something shrink - either you reduce the physical size, and the mass stays the same, in which case the Enterprise on the table now has neutron-star level gravitational pull, OR you delete 99% of the atoms and keep 1 out of every 100 (sampling), like reducing a bitmap image in size. And just like that image, when the Enterprise went back up to full scale, everything would be "chunky."
The City on the Edge of Forever - S1-E29
Corrected entry: On the ship, McCoy gets injected, runs down to the Transporter, and beams to the planet. On the surface, he has a phaser, when he didn't have one when he beamed down.
Correction: He took the phaser from transporter chief Kyle before beaming down.
So he did... I stand corrected.
The Gamesters of Triskelion - S2-E16
Corrected entry: As Shana watches Kirk, Uhura, and Chekhov disappear, when the camera is in a close up on her face, the vertical seam where two wall sections meet is visible.
Correction: It is more likely to be one of the numerous torch poles surrounding the arena.
This Side of Paradise - S1-E25
Corrected entry: Spock is wearing his normal blue uniform when shot with the "happy spores" from the strange plant. The next scene is with Kirk inquiring about Spock's location to which he is told nobody has seen him. Spock somehow manages to find some green overalls out in the meadows when we switch back to him. (00:17:40)
Correction: Remember, Leila took Spock to that location for the express reason of having him infected. She likely brought civilian clothes for him, knowing he would no longer want to wear his uniform.
Corrected entry: Glasses worn by a transporter crew member disappear as Pike and crew are beamed down. (00:37:06)
Correction: 1) There is plenty of time for him to remove them while the landing party steps onto the platform. 2) He is wearing them while making notes on a pad. Obviously, he only needs them for reading/writing.
Corrected entry: While Lieutenant Galloway is coming into sickbay and dies there is a window in the hallway with window blinds, and through this window you can see some of the production staff in regular clothing talking.
Correction: The "production staff" is dressed in Star Fleet uniforms. They are not just standing around talking but working with something. There are even flashing lights in the background. The window is looking into a medical lab. Besides, the supposed error defies reason. Why would they build a window into a set and put nothing behind it?
Tomorrow is Yesterday - S1-E20
Corrected entry: When the Enterprise is slingshotting its way back to the "present" it uses the computer to deposit the two men at different times, The Enterprise is traveling backwards in time, so will logically meet the time when the guard was beamed up first, not after Christopher is returned to his cockpit. So the order is wrong. Should be guard then Christopher, not Christopher then guard. (00:43:15)
Correction: They are moving backwards in time as they approach the sun, but after the slingshot breakaway they are moving rapidly forward in time. Spock even says the chronometer is moving forward again, and then Kirk asks if they have the exact chronometer reading before redepositing Captain Christopher and the Sergeant. So the order depicted in the episode is actually the correct order.
Where No Man Has Gone Before - S1-E4
Corrected entry: If the point was to repair the ship, and maroon Gary Mitchell, then why have Lee Kelso wire a destruct button, thereby threatening Gary's life and placing Lee's life in jeopardy when Gary's powers could overcome him? If they were afraid Gary would become too powerful left on his own, then marooning him should not have been an option.
Correction: It's explained in the episode that the plan is to maroon Mitchell there, but Kirk wants a backup in case they aren't able to escape or Mitchell becomes too powerful.
Corrected entry: After Kirk and Spock's identities are revealed, they are taken to a prison cell. However, the Organians are a race of pacifists who abhor any act of violence - this should presumably include the act of incarceration. As such, there should be no prisons on Organia. Moreover, the Klingons are not stone masons; the prison cell shown in the episode is architecturally consistent with the other buildings on the planet so it was not constructed by Klingons (especially so quickly).
Correction: This is purely speculation. Being pacifists doesn't preclude them from having a jail cell, especially since the entire town was created for the benefit of outsiders.
Corrected entry: Ben's plan is absurd, hiding and pretending to be dead in a ship of over 400. Eventually Ben has to eat or use the bathroom, someone would see him.
Correction: His plan is absurd, which leads to him being discovered, exactly as you say. He's shown to be deranged, if not insane, so this isn't a plot hole, it's a plot point.
Tomorrow is Yesterday - S1-E20
Corrected entry: When the tractor beam crushes the fighter jet, Spock asks captain Kirk, "do you want me to turn off the tractor beam?" Why would Spock ask a stupid question like this?
Corrected entry: Scotty is cutting through the bulkhead to get to the controls to open the door to get to engineering, but considering the time left, why not just blast through the door itself?
Corrected entry: When Spock takes Captain Pike out of the briefing room, Pike appears, via the viewscreen, on Talos IV in the very next shot. There is no possible way Spock could have gotten Pike to the transporter room that fast.
Correction: Not a mistake. Pike's appearance on the screen is of his younger, uninjured self - obviously one of the Talosians' illusions. So they "jumped the gun" a bit by showing him on the planet before his actual arrival, but this image is only for illustration to the people viewing, so it doesn't matter.
This Side of Paradise - S1-E25
Corrected entry: A captain from the 2200's owns Samsonite luggage from the 20th century.
Correction: The original Star Trek series was actually produced on a very limited budget of about $250,000 per episode, and many of the props were re-purposed items from thrift stores. It was not uncommon to see all sorts of 20th Century items (clothing, luggage, dining room sets, household spray bottles, salt shakers, et cetera) on any given Star Trek set. Keep in mind that those items were chosen because they were rather futuristic in appearance to audiences of the mid-to-late 1960s, even though they appear whimsically anachronistic to our eyes, just 50 years later.
Also the characters have access to replicators and super computer databases. The cases could be 23rd century reproductions, classic antiques, etc.
Corrected entry: The whole plot centers on the crowded conditions of the planet. The people are literally bumping into each other. Even if they had the blueprints to build a full size model of the Enterprise, there would be no room for it.
Correction: That's actually a plot point of the episode; that they were so desperate for this to work they were willing to sacrifice that much space.
Corrected entry: Gary Seven transported down to earth using the enterprise transporter system. Because of this he should re materialise in the same fashion as normal, yet for some unexplained reason he comes from his safe in a cloud of blue gasses. (00:10:30)
Correction: True, he used the Enterprise transporter, and people usually can't move when re materialization occurs. However, Gary Seven, with his advanced knowledge, would know how to work the transporter, target his safe/transporter (with vastly superior alien technology), and be able to walk out before the normal cycle was finished. This is due to the alien transporter being superior. In later incarnations, people can move while being transported.
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.
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.
Corrected entry: The Ekosians have a modern society with large flat panel screens, but somehow haven't mastered color broadcasting.
Correction: This is due to when this show was made and the status of technology of the time. By this same logic, you can say the entirety of Star Fleet is behind with their technology is some respects. Like the simple blinking light displays of their computers and the monotone robotic voice of their computers.
Correction: First off, we do not know how "heavy" the rod is, but could have been handled easily by Kirk due to adrenaline from the fight. Second, in context of the story of Khan and his people being genetically engineered super humans, Khan would be able to absorb some of the blows Kirk delivers to him.
Scott215