Factual error: Anne Frank received her diary on her birthday, and started writing on it 1 month before she went into hiding. In the movie however, she is presented with the diary on the first she arrives at the hiding place.
Suggested correction: Since this movie is based on actual events and not considered a documentary, then the film-makers are allowed to change things to their liking.
While I feel like this sort-of correction could apply to certain elements of movies based on true stories like dramatized scenes (since there has to be some condensation of time and some elements boosted for drama, which can be chalked up to filmmakers changing things), I think a film based on a true story contradicting a known hard fact like this should 100% count as a mistake. Otherwise, you could just as easily argue that any factual error in any film is invalid because the filmmakers are "allowed to change it."
Other mistake: When Anne and Peter are looking at the stars, Anne points to a star and Peter knows what star she's pointing to. It is impossible to point to a star and have someone else know exactly what star you're pointing to. Try it.