Continuity mistake: Harry buys the book "One Thousand Magical Herbs and Fungi", but later, the title changes to "One Hundred Magical Herbs and Fungi".
Continuity mistake: While being sorted into houses, Harry looks up at the Sorting Stool, and there are only three people left to be sorted. Professor McGonagall then calls out the names of four more kids.
Plot hole: When Malfoy gets into trouble while trying to catch Harry with Norbert, Professor McGonagall dismisses his claims as "utter rubbish", and a "cock and bull story." To prove his story was true, Malfoy could have shown her the letter Ron received from his brother Charlie (which Malfoy accidentally received when he borrowed a book from Ron), which detailed their plan to deliver Norbert to Romania.
Plot hole: On page 56 of the original UK edition, Harry overhears a witch complaining about the price of something as being "seventeen Sickles." There are seventeen Sickles to a Galleon, so a witch who is familiar with the Wizarding world (as she obviously is, given that she knows that price to be unusually expensive) would say "one Galleon" instead. This was changed to "sixteen Sickles" in later editions for this reason. Page 72 in the American version.
Factual error: When Harry is with the Dursleys in the run-down shack, he realises that Tuesday is his birthday. However, in 1991, July 31st was a Wednesday.
Other mistake: On page 221 of the American hardcover, the third paragraph begins "...wished him luck outside the locker rooms the next afternoon." But Harry couldn't have just been getting to the locker room in the afternoon; Quidditch matches take place in the late morning: the school teams are usually dressed and already on the pitch by 11:00 am.