Visible crew/equipment: After McCoy examines Charlie and they talk about how Charlie learned to talk by just listening to the ship's tapes, when Charlie stands up the two actors' marks can be seen on the floor - the short one for Charlie and the longer one for McCoy, where they both will stand momentarily. (00:04:56)
Factual error: Towards the end of the show the Enterprise is leaving Earth orbit and heading towards the sun. We see the Earth diminish and the moon appear looking exactly as it does from Earth. From this angle we should be seeing the "dark side" of the moon, which looks completely different. (00:40:50)
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)
Plot hole: Pike says he doesn't want women on his bridge, Number One being the one and only exception, and he keeps ordering Colt off it. His apology to Number One indicates that A) he doesn't think of her as female, and B) she's the only exception to his rule. So how does he overlook the very female crew-woman seated at the science station? (00:06:55)
Other mistake: The closing credits of thirteen episodes in season 1 have the word "Script" misspelled as "Scpipt" for the episode's script supervisor, either George Rutter or Billy Vernon. The episodes are: "The Galileo Seven"; "The Squire of Gothos"; "Arena"; "Tomorrow is Yesterday"; "The Return of the Archons"; "Space Seed"; "A Taste of Armageddon"; "This Side of Paradise"; "Devil in the Dark"; "Errand of Mercy"; "The Alternative Factor"; "The City on the Edge of Forever"; "Operation - Annihilate!"
Continuity mistake: When Kirk exits the turbolift he sits in the captain's chair, and Yeoman Smith stands behind him with barely any space between them, but in the shot facing the main viewscreen Smith is gone, and in the next shot she reappears right behind Kirk again. Smith continues to disappear and reappear in following shots. (00:04:00)
Visible crew/equipment: When Dr. Van Gelder tells Kirk that he wants asylum and his word that he won't be taken back to Tantalus, in the wideshot from behind Kirk as he moves to his right the two tape marks can be seen on the floor beside Van Gelder's feet.
Visible crew/equipment: After Kirk's briefing regarding Mitchell's abilities, when Spock and Kirk are alone just as Spock says that they'll never reach an earth base with Mitchell aboard, the boom mic casts a shadow overhead until Spock steps forward, and a bit can be seen again when Spock tells Kirk that it's his only choice. (00:24:50)
Continuity mistake: When the Thasians restore Yeoman Rand on the bridge she's barefoot, but when Charlie begs Kirk not to let the Thasians take him because he can't live with them anymore, we see Rand wearing a white fluffy slipper (which she wasn't holding when she reappeared), then she's back to being barefoot again. (00:44:42)
Visible crew/equipment: After Uhura tells Kirk that "Captain Ramart of the Antares is on D channel," Kirk and Charlie head to the bridge, and when it cuts to Uhura the actor's tape mark can be seen on the floor behind her, where Charlie will stand when he steps out of the turbolift.
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.