Continuity mistake: When Harry and Hermione leave from the hospital wing using the Time Turner, Dumbledore says it is ten minutes until midnight, but on the way back to the ward after they rescue Sirius, they hear Dumbledore say to the other versions of them that it is five minutes to midnight. (Corrected in later versions.)
Continuity mistake: Arthur Weasley says that Ron and Harry have both been in the Forbidden Forest twice. Harry has gone in twice, but Ron has only gone there once, in The Chamber of Secrets while following spiders. (This differs from the movies when Ron is given detention instead of Neville).