Other mistake: At the end of the film when they arrive in NYC looking for the library, we know that they survived because they are inside with a roaring fire burning. But where is the smoke up above, as Jack Hall approaches? There must be a chimney, or else they would have all died of asphyxiation.
The Day After Tomorrow (2004)
Ending / spoiler
Directed by: Roland Emmerich
Starring: Dennis Quaid, Jake Gyllenhaal, Ian Holm, Emmy Rossum, Sela Ward, Dash Mihok, Jay O. Sanders
Jack Hall and Sam both survive the storm. Jack finds Sam in the library, they get rescued by some government helicopters and are flown back to Mexico. Laura Chapman also survives. Most of the people in the Northern States / Canada / Northern Europe die during the storm (including all the people who leave the library during the storm to walk south). The US president also dies. The rest flock down to Mexico which only allowed the Americans in because they nullified all the Latin American debt.
Rolf Campbell
Sam Hall: Look, I got every question right on the final, and the only reason Mr. Spengler failed me is because I didn't write out the solutions.
Jack Hall: Why not?
Sam Hall: I do 'em in my head.
Jack Hall: Did you tell him that?
Sam Hall: I did. He said he didn't believe me. He said that if he couldn't do them in his head, then I must be cheating.
Jack Hall: Well, that's ridiculous! How can he fail you for being smarter than he is?
Sam Hall: That's what I said.
Jack Hall: You did? How did he take it?
Sam Hall: He flunked me, remember?
Trivia: There is a party at J.D.'s school after the academic decathlon. Most of the students are wearing name tags. Sam's name tag says "Hello my name is Yoda." (00:21:50)
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Suggested correction: As already corrected, just because we can't see an outlet for the smoke doesn't mean there isn't one. White smoke against white snow is very hard to see.
Nik Rolls
But they were still burning the books, which meant the smoke should be black, if they stop burning the books, the smoke would have been white, which isn't the case in the movie.
Just looked at a boatload of videos of burning books, including one in a fireplace, and the smoke was indeed white.