Revealing mistake: "The Cage": In the first illusion, Vina runs down the path from the fortress to Pike. When we cut to close-ups, they're both suddenly standing much closer to the building than before, and the fortress has changed color from brownish orange to white.
Factual error: When they are searching for Finney hidden somewhere in the ship, all ship noises are deadened, and the heartbeats of those on the bridge are muffled by McCoy. In order to locate Finney's heartbeat the ship's auditory sensors are magnified by "one to the fourth power". That's 1x1x1x1 = 1, ie no magnification.
Factual error: Edith Keeler says to McCoy, "My young man is taking me to see a Clark Gable movie." In 1930, Clark Gable was an uncredited bit player who had last made a film in 1926 - Edith, a New York charity worker, would not even have encountered his name.
Continuity mistake: At the hearing in the final scene, there are two bits of debris of some sort (small, black and roundish) littering the floor at the bottom left of the screen. Whatever it was disappears when Scott, Spock, Kirk and McCoy get up to leave the room.
Continuity mistake: When Kirk exits the turbolift he sits in the captain's chair, and Yeoman Smith stands behind him with barely any space between them, but in the shot facing the main viewscreen Smith is gone, and in the next shot she reappears right behind Kirk again.
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