In the American paperback page 161, when talking about the old Defence Against the Dark Arts teachers, Harry says, "One sacked, one dead, one's memory removed, and one locked in a trunk for nine months." referring to Lupin, Quirrell, Lockhart, and Moody respectively. However, according to PoA American paperback page 423, Lupin did not get sacked, he resigned. Although, Harry could have interpreted Lupin's resignation as forced by Snape's revelation of his lycanthropy, and therefore considering it the same as a sacking. Also, Fred does not mention either of his first two DADA teachers, even though in Half-Blood Prince, though it is possible that those two simply resigned and nothing particularly bad happened to them, thus no mention.
In Chapter 3, when the Advance Guard arrives at 4 Privet Drive to take Harry to 12 Grimmauld Place, Harry is already in trouble for casting a Patronus Charm in the presence of a Muggle. Yet, Tonks casts several spells (Lumos, a packing spell, Scourgify, Locomotor Trunk) and Moody casts a Disillusionment Charm on Harry while they are still at 4 Privet Drive. Lupin had clearly stated that they were not using the Floo Network because they were being watched (by the Ministry), so of course the Ministry was not aware of any Wizards that are allowed to do magic were inside Harry's house. If the Ministry can detect magic, and Harry is the only known wizard in Little Whinging, then he should have either had another owl sent from the Improper Use of Magic Office or the uses of those spells should have been brought up at some point during his trial. Possible explanations include the fact that there were no Muggles present at the time, or that unlike Dobby, magic used by registered wizards does not activate the Trace.
Sirius Black told Harry Potter that Bellatrix ran in the same crowd as Severus Snape while at Hogwarts, but her date of birth makes this impossible. Bellatrix would have attended Hogwarts from 1962 to 1969, or possibly 1963 to 1970, depending on which month in 1951 she was born in, whereas Snape began his schooling in 1971. This may simply be an error, as J. K. Rowling has admitted that math is not her strong suit. Another possible explanation could be that both Bellatrix and Snape went around with the same type of people, some of whom may have overlapped depending on age.
Ginny Weasley's birthday is on the 11th of August, the day before Harry's trial. The day before the trial is mentioned, but Ginny's birthday is not.
During Harry's hearing, Cornelius said that he blew up his aunt three years ago. However, the incident when Harry inflated Marjorie Dursley occurred almost exactly two years previously.
In chapter 9, Ron's prefect badge is described as scarlet and gold. Page 162 of the American paperback states: "A large P was superimposed on the Gryffindor lion. He had seen a badge just like this on Percy's chest on his very first day at Hogwarts." However, Percy's badge in Philosopher's Stone is described as silver with a P on it. (Later editions of the first book are fixed.)
In chapter 9, Mrs. Weasley says that everyone in the family has been a prefect, but Charlie was a Quidditch Captain. It is possible that she was including Charlie, as Hermione says in the sixth book that Quidditch Captains have equal status with prefects. It is also possible that Charlie was a prefect in addition to being Quidditch Captain.
During the meeting in the Hog's Head, Dennis Creevey shows up for the meeting. However, in Harry's fifth year, Dennis would only be a second year, and therefore would not be able to visit Hogsmeade. He could, however, have snuck out of the school with his brother.
After Harry has seen his father bully Snape in a memory, he remembers Professor McGonagall saying that James and Sirius were troublemakers at school, but no more so than the Weasley twins. This is incorrect. She said in the Prisoner of Azkaban that she had no memory of anyone else being so troublesome, and Hagrid said Fred and George could have given them a run for their money. One possible explanation is that McGonagall's earlier statement was hyperbole.
In chapter 30 of the American hardcover, Harry and Hermione find seats in the topmost row at the Quidditch match. But when Hagrid comes to tell them about Grawp, he squeezes his way through the row behind them. If Harry and Hermione are in the topmost row, there cannot be a row behind them (corrected in later editions).
In Chapter 31 "O.W.L.s", it is stated that the practical Astronomy O.W.L. began at 11:00 pm, and Harry observed Venus one hour later (12:00 am). However, Venus can only be observed shortly before sunrise, or shortly after sunset,[2] it can never be seen at midnight. Harry was also filling in his star chart with the stars in the constellation of Orion, however Orion would have set before 11:00pm on that date.[3] Also, Hogwarts is somewhere in the Highlands of Scotland (according to the movie of Prisoner of Azkaban, it's near Dufftown in Moray); at that latitude, in the two months either side of June 21, the sky never gets completely dark. There is at least one website showing that sunset on the day of the examination would be about 11pm — the time the examination is supposed to start. It would be unlikely to be dark enough to observe any but the brightest stars.
In chapter 37, after Sirius' death, Harry reminisces about when Sirius watched him play Quidditch in Harry's third year. Harry wonders if Sirius had come to see if he was as good a player as James had been, and regrets never having asked him. However, in Prisoner of Azkaban Sirius specifically tells Harry that he did watch him for that exact reason, and that he was as good as his father. It is possible that Harry could have forgotten this. This is quite possible, as it had already been nearly two or so years, though it does seem odd that he would forget such specific praise from someone whom he cares about so deeply.
During the Ordinary Wizarding Level examinations, Hannah Abbott was doing her transfiguration practical at the same time as Harry Potter. This is odd as the examinations are done by surname, meaning that Hannah should have finished a while ago, unless she was a rather incompetent student, or unless she had a fit of anxiety in the middle of the examination and had to be calmed, which could take time, and then resume the exam when Harry started his.
In an error unique to the U.S. audiobook editions of Harry Potter and the Order of the Phoenix, when Harry first arrives at 12 Grimmauld Place following his vision of the attack on Arthur Weasley, the line "Back again, the blood-traitor brats! Is it true their father's dying?" is rendered in the loud, screechy voice of Sirius Black's mother. Based on context clues, however, particularly the fact that this line is immediately followed by Sirius shouting "Out!" and Kreacher shuffling out of the room, it seems clear that it was actually Kreacher that uttered the insults, not Mrs. Black.