Character mistake: When they're on the island and the INGen helicopters are flying in, Jeff Goldblum takes the binoculars and looks through the wrong end. (00:32:30)
Character mistake: When Ripley asked the doctor how they "got" her, he replies from blood samples on Fury 16. This is in reference to the planet in Alien 3, but it was called Fury 161. (00:11:00)
Character mistake: When Troy is getting the bomb ready, the screen shows it will blow in 216 hours, which is 9 days. Yet the agent tells Archer it will blow in 6 days.
Character mistake: When the police scan Leeloo the first time, the computer reads "Commencin" instead of "Commencing."
Character mistake: When they first receive the alien signal, they decode it and play it as a TV signal which shows Hitler speaking at the opening of the 1936 Summer Olympics in Berlin. Kent translates what Hitler is saying as "I declare the Games in Berlin, at the celebration of the first Olympics of the New Era, as opened." Hitler actually says "the *eleventh* Olympics of the New Era." The "New Era" doesn't refer to some Nazi concept, it's used to separate the modern Olympics from the ancient ones in Greece.