Continuity mistake: In June, Fred and George Weasley find out they have scraped "a few O.W.L.s apiece". However, in subsequent books, it is firmly established that O.W.L. results are sent home by owl and are not received until August.
Continuity mistake: On page 341 (American hardback) "it says "Ron crawled to the four-poster and collapsed onto it". But when Professor Lupin comes in, it says "his eyes flickered over Ron, lying on the floor". This could not be, because Ron is still in the bed.
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).
Factual error: Chapter sixteen (Professor Trelawney's Prediction) takes place in June 1994. In the beginning of page 341 (Bloomsbury edition) of that chapter, Harry Potter reads a note from Hagrid and says, 'Buckbeak's appeal - it's set for the sixth.' The night after the Hippogriff's appeal, Remus Lupin is forced into a werewolf form by the full moon, which means that this happened on the night of June 6th, 1994. The web page http://www.hp-lexicon.org/timelines/main/timeline_1990s.html#1994 also backs this up. However, a brief look at lunar phase calendar sites such as http://stardate.org/nightsky/moon/index.php?month=6&year=1994 and http://mysite.verizon.net/bonniehill/pages.aux/lunar/lunar.phases.1994.html definitely shows June 9th, 1994, as a new-moon night, which means that a full moon could not possibly rise three days earlier.
Continuity mistake: At the beginning of the story Harry is reading 'A History of Magic by Adalbert Waffling'. However, from the Philosopher's Stone we know that 'A History of Magic' was written by Bathilda Bagshot and that Adalbert Waffling wrote 'Magical Theory'.