Rephrasing, do any of the Harry Potter books create situations which conflict with earlier and/or later canon? What are the more conflicting or note-worthy examples?
It's been quite a few years since I last browsed the books and I never was a cult-tier enthusiast, but as the saying goes, the devil lies in the details.
Yes, definitely.
What follows is not an exhaustive list, but should give you some idea of the sort of discrepancies and mistakes that exist.
The most significant example comes from Goblet of Fire. In an early printing of the book, in the scene where Voldemort’s victims emerge from his wand, James came out before Lily, despite Lily having been killed more recently. This was revised in later printings.
See the question Why did Harry's father emerge before his mother in HP and the Goblet of Fire? for more details.
@DVK asked a question about six months ago about discrepancies between the main seven books, and the supplementary books Fantastic Beasts and Where to Find Them, Quidditch through the Ages and The Tales of Beedle the Bard.
My answer to Are there any discrepancies between HP1-HP7 and supplementary books? contains a list of the slip-ups that I know about.
Pottermore has also thrown up some discrepancies between the books, and the “word of God” additional text and interviews by JK Rowling. See @Slytherincess’s Meta question What is the best way to deal with complicated canon discrepancies when answering questions? which highlights one such example.
The Harry Potter Wiki isn’t generally considered canonical or accurate on this site, but their list of mistakes in the Harry Potter books is probably the closest to an exhaustive list that you’ll find. (Asking for the complete list on this site would almost certainly be closed as “too broad”.)
A running joke on this site is that JK Rowling’s maths is patchy, at best.
For example, dates just don’t work. We know from Nearly Headless Nick’s deathday party in Chamber of Secrets that the books take place in the 1990s, but then weekdays don’t match, and the time between dates isn’t consistent with any known calendar. (See my answer to Do wizards use the same calendar as muggles? for one such example.) Related to dates are ages, which are sometimes inconsistent from book-to-book. The HP Wiki has a more complete list of dating contradictions.
From an FAQ page on JK Rowling’s website, addressing one particular dating mistake:
Maths is not my strong suit (though it's better than my geography, as those who have found the most recent Easter Eggs might already know).
Another fairly obvious one is the size of the castle compared to the yearly intake. The school is far too small to merit such large premises, and the size of the magical population in Britain is unsustainably small.
Searching this site is bound to find you other examples of JK Rowling’s dodgy maths.
Finally, JK Rowling has acknowledged, on multiple occasions, that there are mistakes in the books. From another FAQ page on her website:
How do you remember everything from different books when you are still writing the HP series?
As obsessive fans will tell you, I do slip up! Several classrooms move floors mysteriously between books and these are the least serious continuity errors! Most of the fansites will point you in the direction of my mistakes. But the essentials remain consistent from book to book because the story has been plotted for a long time and it is clear in my mind.
The most common type of contradiction is when a statement in an interview with Rowling is contradicted by a later book. Here are some famous cases.
Who in the Potterverse manages to do magic only quite late in life? Rowling said at one point that “there is a character who does manage in desperate circumstances to do magic quite late in life, but that is very rare in the world I am writing about”, but had later changed her mind.
How can JKR's rules for Secret Keeper be reconciled between Deathly Hallows and FAQ? Rowling's old webside contains an entry on what happens when a secret-keeper dies.
There was a third important one but I forgot.
https://scifi.stackexchange.com/a/28035/4918 At one point Rowling had claimed that she'd already written the last chapter of the last book, to have a goal she's writing towards, and that the last word in this was “scar”.
The one I found was when Sirius shouts "KREACHER!" in Order of the Phoenix, but Kreacher doesn't show up.
In HBP, Dumbledore clearly states that everything (including Kreacher, along with the house and everything inside) was Sirius', as he was the only male in the Black family. This means that others like Bellatrix and Narcissa were not qualified to order Kreacher around, at least over Sirius. So they couldn't have made Kreacher disobey a direct order (summons) from Sirius.
Remember that when Harry screams Kreacher's name in HBP or DH, Kreacher appears suddenly, as he is not allowed to ignore the summons, and he has to submit immediately. Also, Kreacher "had to" Apparate out of the Cave, without even thinking about being able to(!), just because his master (Regulus) asked him to!
I have already countered the argument of others (like Bella) not allowing Kreacher to answer the summons. To counter the argument that "maybe Kreacher didn't answer on purpose, and then he had to punish himself for it, just like Dobby did", I have to refer you to the fact that when Harry tells Kreacher to shut up in HBP, he gags. Later, when Harry tells him that he is not allowed to communicate with Malfoy, Kreacher doesn't (despite the fact that he would rather break his own arm, than to betray the pure blood, lovely Draco!) as Kreacher is not allowed to disobey a direct order.
Dobby never disobeyed a direct order. He was just badmouthing his masters and he was allowed to do so, followed by punishing himself. The Malfoys wouldn't dream of their house elf spying on them for Harry, so they never asked him to never visit him.
To sum up, Kreacher not answering to Sirius' summons contradicts the rules and laws that Dumbledore states in the beginning of the sixth book.
TVTropes has a good example on a retcon:
In the first book Rowling had Voldemort tell Harry that his father "put up a courageous fight" before he died, and there was no reason for him to lie to Harry at this point (although it's not inconceivable that he was exaggerating). Seven books on, James Potter is killed in flashback without raising so much as a finger against Voldemort, though James did try to hold him off, but was killed quickly, having forgotten his wand.
The Prefects, according to Order of the Phoenix, cannot dock house points, however in Chamber of Secrets, Percy, a Prefect, docks house points from Ron.
