I'm guessing that later in the story, Harry will be framed and sent to Azkaban, allowing his hitherto unknown twin who’s the actual Boy Who Lived to take his place, get adopted by Snape and become Head Boy, upon which he hooks up with Hermione (who turns out to be really a pureblood) at the annual Yule Ball and they have lots of rampant sex in the Head Boy and Girl’s private quarters, and meanwhile Draco discovers that he’s part-Veela and hooks up with an American exchange student who’s a newly discovered species of super-witch with an anachronistic taste in clothes and music, and they go off and fight the resurrected Salazar Slytherin together.note None of this actually does happen, but it wouldn’t have been a surprise if it had.
Designated Hero: Harry, in the new timeline, he destroys the Weasleys’ lives for things they haven’t actually done yet (including feeding Percy to Fluffy and rendering Ron sterile and unable to perform magic, as well asrendering the entire family homeless by seizing the Burrow even though Arthur, Bill, and Charlie never do anything wrong even within the story) and sees nothing wrong with doing so. Hermione, at least, does show a little angst and remorse.
Fridge Logic: So why would Voldemort protect parts of his soul with items that can be destroyed for a nominal fee?
Once Harry and Hermione meet again and realize that both of them have their memories from the previous timeline, they begin discussing what to do. Harry's understandably worried about how Dan will take Harry being engaged to his daughter at the age of eleven, noting that Dan "will probably half kill (Harry) before passing him over to (Hermione's) mum to finish the job." Hermione points out that she'll be twelve in a couple weeks, and Harry sarcastically suggests telling her parents after her birthday.
When Dumbledore asks him for "a quick word," Harry says "Velocity."
The rationale for Umbridge becoming Minister for Magic instead of Kingsley is that the Minister must be a pure-blood. Then Pottermore revealed that the Shacklebolts are indeed an old pure-blood family, and Umbridge’s mother was a Muggle.
Good luck re-reading the bit about the “secret ritual” for transferring the Horcrux soul fragment into a pig and not thinking of piggate.
Snape is, if anything, more sensible and reasonable than he is in canon, which doesn’t stop the story from going on about how terrible he is.
As far as Ron and Percy in the new timeline are concerned, Harry and Hermione are a pair of stuck-up bullies who’ve got it in for them and their family for no apparent reason, yet we are supposed to think they’re terrible people for resenting this.
Never Live It Down: Hermione, to many readers. For all the later chapters insist that she’s as badass as she is in canon and then some, though not showing us quite so much, she will always be the person who got overpowered twice by a shit wizard. That she’s subject to Chickification throughout only contributes to this.
Strawman Has a Point: Any time someone (usually Molly or Snape) goes off on one about how terrible Harry and Hermione are in the new timeline.
Unintentionally Unsympathetic: Once Harry and Hermione are back in time, they mercilessly bully the people who would have hurt them in the original future despite said harm having not having been done yet and despite the very nature of their actions preventing the harm from ever coming to pass, and act like smug little twits about it all.