The Thestrals are revealed to be the ones pulling the supposedly horseless carriages from the third and fourth books. They were never mentioned up until this book and Harry didn't see them on his way back from Hogwarts the previous year after watching Cedric die. The only purpose they really served was to give Harry and his friends a ride to the Ministry of Magic office. Word of God is that they don't appear because Harry needed time to process Cedric's death, but regardless of that, with multiple students boarding the carriages each year, it stretches belief that no one had discovered the thestrals even by simply unknowingly bumping into them.. They are mentioned in Fantastic Beasts and Where to Find Them... but that wasn't published until after Goblet of Fire.
Apart from people controlled by the Imperius curse being released when Voldemort was defeated, the concept of spells no longer working when their caster dies isn't mentioned anywhere else in the series. There are countless examples of spells still being in effect for years after their caster died. Interestingly enough, this concept is used in both the book and the film, but in different ways: in the book, it's Dumbledore's Petrification spell on Harry breaking after his death at the Astronomy Tower; in the film, it's Slughorn's story about Lily Evans's fish.
Central as it might be for the last two books in the series, the very existence of Voldemort's Horcruxes can feel rather jarring. The previous book made a big deal out of the revelation that Harry and Voldemort were connected by a prophecy, and even if the latter's ambiguous outcome was nebulous from the start, it was presented more or less clearly as both the beginning and end of their saga. True, Riddle's diary from the second book would turn out to be a Horcrux, but this can add to the suddenness considering that until this point no attention had been given to the item's nature, not even by Dumbledore himself, which implied that the diary was nothing more than a random MacGuffin cursed by Voldemort's formidable magic. Even Voldemort's line in The Goblet of Fire about his own advance towards immortality was well explained by its own context, namely the fact that he had acquired the dark power to live as a spirit possessing people to escape death and finally recover his own body. All those things can give the impression that the Horcruxes were a plot-point which Rowling only added as late as this very book and whose foreshadowing was built over rushed retcons. (Apparently Chamber of Secrets included some more Foreshadowing on this, but Rowling's editor nixed them as she had yet to achieve her Auteur License.)
The Deathly Hallows themselves and the entire new series of mysterious artifacts feels like this to some readers, who felt that Half-Blood Prince had established the Horcruxes as the main MacGuffin to hunt down and were amazed that Rowling introduced a new mystery on top of it (especially one related to a complex history involving Dumbledore, his friend-turned-dark wizard Grindelwald, and the Elder Wand, one of the Hallows and an unstoppable weapon whose nature turns the final duel with Voldemort in Harry's favor). They felt that if Rowling had introduced this in Book 6, or at least Foreshadowed it, it would have worked better. It's true that Harry's invisibility cloak never tearing or falling into disarray was mentioned before, and it's also true that Harry is quite reasonable in taking the power of his Cloak for granted, since he has no other frame of reference, but various other characters do have a frame of reference — Mad-Eye Moody, who owns two, springs to mind — and none of them ever comment on its status or unique qualities. Similarly, the story of the Hallows is a fairy-tale familiar to all wizards (well, those not raised by muggles, anyway), but nothing about is told it until halfway through the book.
Within the Deathly Hallows, the Resurrection Stone in particular. After so many installments hammering down the message that death is something inevitable that must be deal with rather than avoided (with even ghosts of all things being shown as proofs of it rather than the opposite), now it turns out there is a powerful enough magic in the Wizarding universe that can summon the souls of dead people, and not those who choose to stay in the world as ghosts, but those who chose to step into the afterlife. In fairness, it's not a perfect solution, given that the "resurrected" souls turn out to be intangible, disembodied spectres rather than true resurrected people; The Tale of the Three Brothers implies that those souls which depart into the afterlife generally no longer want to remain in the mortal world anyway, and Harry's consequent letting go of the stone in the Forbidden Forest is perhaps meant to reinforce the point that death is inevitable and can only be accepted, seeing as there's no perfect remedy for it regardless. However, the mere inclusion of the stone in the first place can still come across as a bizarre twist and a Broken Aesop at it.
The concept of Wand Lore. It's true that in the first book "The Wand Chooses the Wizard" indeed, but the idea of the wand changing allegiances during a wizard duel was never suggested once even if Wizard dueling was both shown and discussed countless times in the earlier books. The previous Horcrux plot showed Harry that he could stop Voldemort from reviving again and again, but this did not help his chances in fighting the man in person, so the Wand twist mostly feels like a cheap and obvious way for Harry to defeat Voldemort in a single duel, especially without killing him and by using his signature "Expelliarmus."
Harry's entire tragic backstory was kick-started when his parents chose Peter Pettigrew as their Secret Keeper to entrust their location to, a requirement for the Fidelius Charm used to conceal their home from Voldemort. It made a certain logical and poetic sense that the confidant would need to remain outside the effective area of the spell, since it's a common convention that magic requires some kind of sacrifice or tangible obligation. Then, in this book, another character casually mentions being the Secret Keeper for their own dwelling, showing that this was actually possible (also prompting the question why couldn't Harry's parents do the same thing).
Although Harry Potter and the Goblet of Fire had established that Harry and Voldemort now shared Lily's sacrificial protection due to the Harry's blood having been used for Voldemort's resurrection, this book has Dumbledore revealing that the bond had the unexpected side effect of binding their lives in an one-directional way, meaning Voldemort cannot kill Harry as long as he remains alive himself. This groundbreaking notion, which allowed Harry to survive the Avada Kedavra that destroyed his piece of Voldemort's soul, was not revealed until the very instant in which it was needed for the plot, and it also retroactively trivialized all of their previous encounters from the fourth book onwards. Even when Harry asks Dumbledore how this could be, the only answer given is a Hand Wave based on the application of some dubious logic to what we knew for sure about their connection, which never included such a possibility (it does fit the theme throughout Deathly Hallows that Dumbledoreisn't as all-knowing and perfect as he looks, but it's undercut by this version of Dumbledore being all in Harry's head). Thankfully, however, this revelation is rather superfluous and easy to dismiss as mere speculation on Dumbledore's part—the film adaptation (perhaps in some awareness of this trope) heavily obscures/omits it altogether, with the implication instead being that Harry's survival is due to the horcrux within him taking most of the impact of Voldemort's killing curse, therefore preventing his own soul from fully crossing to the other side. In fact, Dumbledore lampshaded that Harry and Voldemort bent magic to an uncharted territory not known until then, and he and Harry are aware that Dumbledore's explanations are pure speculation.
The fact that Fiendfyre could destroy Horcruxes was not mentioned until after it burst out and attacked everybody. Hermione handwaves it by saying it was too difficult and dangerous to attempt (and near the beginning of the book she did say that many of the substances that destroy Horcruxes are impractical), since its flames hunt down its victims, though it is also notable that apparently even a dumb student can summon (though not control) it. The fact that the object is a Horcrux that is mentioned as being nearly indestructible several times and which Dumbledore got cursed trying to destroy, to quote Ron Weasley, "really gives a feeling for the scope and tragedy of the thing, doesn't it?" The film remedies this by having Harry stab the diadem with the Basilisk fang before Ron kicks it into the fire just to be safe.
Ron enters the Chamber of Secrets... by imitating parseltongue. While he had been shown to have a skill with impressions occasionally before, the idea he can perfectly imitate an inhuman language well enough to fool the Chamber of Secrets after hearing it a couple of times years apart seems far fetched. The film tries to explain this by saying Harry talks in his sleep, which if anything only makes it even weirder.
The Deluminator comes off a bit like this, as its previous appearances gave no indication that it could be used the way it is in this one, but it's less so compared to the other objects in the books.note It's mentioned that it was invented by Dumbledore himself, meaning no one, besides him, actually knows what the Deluminator does.
Ron's unreasoning prejudice towards Scorpius feels like nothing but a cheap plot device, given that, while he showed plenty of prejudice when he was a teenager, he's now a grown man who's had well over a decade to get over his schoolboy rivalries.
The Sorting Hat putting Albus into Slytherin comes across as this since a) he didn't want to be placed there in the Deathly Hallows epilogue, which the Hat takes into account, and b) he doesn't exhibit any of the personality traits or qualities that the House's members tend to possess. Although (a) is mitigated by the fact that he chose Slytherin over Gryffindor in the play after his friend Scorpius was sorted there, but that makes this plot point a contrivance to put him in Slytherin.
The reveal that Voldemort and Bellatrix had a daughter born before the Battle of Hogwarts. There were no clues about Bellatrix being pregnant in the seventh booknote Ironically, Helena Bonham Carter was pregnant during the filming of Half-Blood Prince, and given that Voldemort planned to live forever, his wanting an heir seems out of character — or even downright incoherent, given that his goal of immortality would essentially eliminate any need of an "Heir". Also, given that it's Voldemort we are talking about, the idea of him showing any kind of romantic or sexual interest in anyone can come across as utterly shocking, especially given how much Dumbledore emphasizes his lack of interest in friendship or human relations of any kind. Later productions try to address this by referring to her as "the ultimate Horcrux", which at least gives practical reasons for Voldemort to have a child, but this just raises the question as to why he isn't still alive if he had a Horcrux that was never destroyed.
The pearl dust in love potions reacting to Demiguise tincture. This lets Albus send a message to Harry and co.
Delphi's hair is never described in the script for Part I, but it helps a character identify her in Part II. Only an issue in the scriptbook version, as obviously in the stage play one can see what her hair looks like from her first appearance.
Polyjuice Potions being created and working perfectly despite not being brewed over the course of a month. Also, the description of Harry's transfiguration wearing off in the climax feels very much like it was initially written as Polyjuice, until they remembered that detail.
The play throws in an entirely new prophecy about Voldemort, giving us absolutely nothing about who made it or when, despite that kind of thing being quite important in the books.
Cedric Diggory pulling an instant Face–Heel Turn over losing the Triwizard Tournament and becoming a Death Eater in the alternate timeline where he doesn't die. It requires quite a suspension of disbelief if you're familiar with Cedric's generous and heroic character from the novels/films, or with the fact that by all prior information Hufflepuffs are literally the last people to become Death Eaters, to the point where it's questionable whether any of them ever did in the original timeline. Basically, Cedric needs to turn evil to advance the plot, so he does... even though it makes no sense in context.
To add even more to this is the fact that Cedric himself viewed Harry as the rightful winner and tried to convince Harry to take the Triwizard Cup alone until Harry insisted on them grabbing it together.
Snape is alive in the darkest timeline... except he was killed by Voldemort himself through Nagini. Even if Voldemort won, Snape would still be dead, because he died before Voldemort and Harry's final fight. Snape is alive simply because without him, the plot would be stuck with no one to assist at Hogwarts.
