Continuity mistake: During Priori Incantatem, Voldemort's victims come out in reverse order. However, James comes out before Lily. He should come out last, because he was killed before Lily. (Corrected in later versions of the book).
Factual error: Harry says to Sirius in one of his letters that Dudley chucked his Playstation out the window. However, Book 4 takes place in 1994, and the PlayStation wasn't launched in Britain until 1995.
Continuity mistake: When Harry is tied up against Tom Riddle's tombstone, it says that his wand is at his feet. Later, Voldemort tells Wormtail to fetch Harry's wand so that they may duel. Wormtail then retrieves Harry's wand from over near Cedric's body.
Continuity mistake: When Fred and George bet on the Quidditch match with Bagman, it says Fred put the paper with their wages in his robes, but Fred was wearing Muggle clothing.
Continuity mistake: When Dumbledore, Fudge, and Moody are talking about Crouch, at one point it says, "said Crouch angrily." Crouch wasn't in the room - they were only talking about him.
Continuity mistake: In chapter 35, the book says '"The Imperius Curse," Moody said.' However, the Polyjuice Potion has already worn off, so it should be Barty Crouch Jr. speaking.