Revealing mistake: After Scotty finally locates Seven on the gantry while he's tampering with the rocket, it cuts to a quick shot of Kirk and Spock, then in the following shot of Roberta when she turns the vault's combination locks, the stunt wire is visible behind her as it moves up to turn the door's wheel handle. (00:35:25)
Star Trek (1966)
41 revealing mistakes in season 2 - chronological order
Is There in Truth No Beauty? - S3-E5
Other mistake: In the final scene, Kirk is still in the transporter room, but does not have on a visor when the ambassador transports out. Even if he did, humans can still go mad if wearing one and that's why Spock operates the transporter. Spock has his visor on, but then you see Kirk walk out of the transporter room without a visor and he is not going mad.
Amanda: And you, Sarek, would you also say thank you to your son?
Sarek: I don't understand.
Amanda: Well, for saving your life.
Sarek: Spock acted in the only logical manner open to him. One does not thank logic, Amanda.
Amanda: Logic, logic - I'm sick to death of logic! Do you want to know how I feel about your logic?
Spock: Emotional, isn't she?
Sarek: She has always been that way.
Spock: Indeed? Why did you marry her?
Sarek: At the time, it seemed the logical thing to do.
Trivia: Gene Roddenberry created the transporter as an easier (and cheaper) way of getting Enterprise crew members onto a planet's surface, rather than landing the ship on the planet.
The Corbomite Maneuver - S1-E11
Question: At the beginning, Mr Sulu calls for Captain Kirk to report to the bridge, but Kirk in sick bay does not get that message. Why?
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.