Harry Potter and the Prisoner of Azkaban

Continuity: Before Harry and Hermione go back in time, it mentions that Buckbeak is tied to a tree. But when they go back in time, Buckbeak is tied to a fence.

Continuity: 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'.

Continuity: 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.

This is the only book in the series in which Voldemort does not physically appear. He is mentioned only in passing in the Shrieking Shack.