Deliberate mistake: Montag's hair gets intermittently shorter, longer and shorter again (and acquires a "cow lick" that wasn't there before) near the end of the film. (Oskar Werner had clashed with Francois Truffaut and deliberately had his hair cut to spite director.)
Fahrenheit 451 (1966)
1 deliberate mistake - chronological order
Directed by: François Truffaut
Starring: Julie Christie, Cyril Cusack, Anton Diffring, Oskar Werner
Revealing mistake: Near the beginning, Montag puts on the fireproof clothing to use the flamethrower. It's really footage of him later taking off the same equipment played in reverse.
Guy Montag: To learn how to find, one must first learn how to hide.
Trivia: The books seen burning at various points in the film include several of Ray Bradbury's novels (Fahrenheit 451 itself is one of these), as well as a French cinema magazine for which director Francois Truffaut once wrote a movie column.