Revealing mistake: While the interior sets for the shuttle craft provided adequate room for the actors to stand, the mock-up built for exterior shots was undersized, and too short to stand up in by several inches. So when entering or exiting the shuttle, the actors always had to duck.
Star Trek (1966)
1 revealing mistake in show generally - chronological order
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)
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.
Who Mourns for Adonais? - S2-E2
Trivia: An ending that was planned but abandoned for this episode would have revealed that Lieutenant Palamas was pregnant with Apollo's child.
Question: When Kirk and crew neutralized all the androids on the planet, what happened to the androids on the Enterprise running the ship?
Answer: If all the humans beamed down and only Androids were on the ship as Larry Mudd said then how did they get back aboard the Enterprise if all the robots were shut down.
Answer: After causing Norman to overload, all of the other androids shut down. The same could be said for the androids on the Enterprise.