Character mistake: The last time Doc tries the defibrillator on Norris, he uses it on the abdomen instead of on the chest. He also positions the pads incorrectly. They should be placed diagonal, with the heart in the middle, not horizontal.
Character mistake: While Khan is "interviewing" Chekhov and Terrell, he stated, "On Earth, two hundred years ago, I was a prince, with power over millions." The official date for this movie is 2285. That would place Khan on earth around 2085 by this statement. However, it is made clear in the episode "Space Seed" that Khan and his followers escaped earth in the year 1996: nearly one hundred years earlier. Quite a way off to be a rounding error. (00:21:45)
Suggested correction: I don't believe the earth year had been established when this movie was made and it was something the franchise applied to itself retroactively later on.
Character mistake: When Deckard is talking to the street merchant trying to identify the snake scale, the identification number he reads aloud is not the number that shows on the monitor. (00:47:30)