Continuity mistake: After their life threatening surgery, Spock and Sarek somehow manage to switch beds between being in surgery and recovering. (00:45:00)
This Side of Paradise - S1-E25
Continuity mistake: As Spock beams up from the planet, Kirk, who is manning the transporter controls suddenly pulls a steel pipe from nowhere. (00:33:55)
Tomorrow is Yesterday - S1-E20
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)
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.