These are mistakes in the Harry Potter series that have been found.  Message me with your find and I will add it to the list and credit you.  Updated June 1, 2014.

Harry Potter and the Sorcerer's/Philosopher's Stone

Sorting hat ceremony, the book says that there were only three students left to be sorted, but four names were shown. (Credited find: Melody MelloLily)

Harry Potter and the Chamber of Sercets

I know of none yet, from this book.

Harry Potter and the Prisoner of Azkaban

I know of none yet, from this book.

Harry Potter and the Goblet of Fire

At the end of the book, Harry gets on the carriages to catch the train, being pulled by the invisible horses.  But because Harry saw Cedric die and was able to see them at the beginning of the fifth book, how come he cannot see them at the end of the fourth book?  (Credited find: Melody MelloLily)

Harry Potter and the Order of the Phoenix

I know of none yet, from this book.

Harry Potter and the Half Blood Prince

I know of none yet, from this book.

Harry Potter and the Deathly Hallows

I know of none yet, from this book.