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.
Star Trek (1966)
1 character mistake in That Which Survives - 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: The Vulcan Nerve Pinch was invented by Leonard Nimoy as a way for Spock to overpower opponents without having to resort to violence.
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.