Deliberate mistake: When Rojan asks Kelinda if she wishes to remain with Kirk, she replies that although Kirk is "most interesting" she wishes to go with him, and the next closeup of Rojan is flipped. (00:48:15)
Star Trek (1966)
1 deliberate mistake in By Any Other Name - 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.
Capt. Kirk: Space, the final frontier. These are the voyages of the starship Enterprise. Its 5-year mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.
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.