Times that Rawling forced the story onto rails that weren't really supported by the canon events....
"Snape is secretly a good guy" is the first thought that came to my mind. His "redemption" boiled down to being "not murderer-evil, just adult-who-bullies-children-evil." The only reason a scumbag like him wasn't the Big Bad was because there was a terrorist running around murdering people.
Related to that, Dumbledore's Death Gambit is probably another example. Rawling needed to get him out of the way so he wouldn't swoop in and be like "I'm fucking Gandalf remember?" when the final battle started up. But rather than have him choke on a pretzel or whatever she had some kind of ridiculous gambit to save Draco and/or Snape's lives from their own shithead choices.
Related to the OP, actually, I'd say the friendship between Harry and Ron. That was the part that got out from under her, because she dropped it, and didn't put the effort into it.
Like... how can I put it, they didn't have DUDEBRO moments where they bumped fists. Ron just stopped bringing stuff to the table. If Hermione was Little Miss Exposition, then Ron was supposed to be the Power of Friendship, but that stopped happening. Like... during those Legilmancy lessons, he should have put his foot down and said, "no. Don't go to those anymore, they're fucking you up. I'll say that straight to Dumbledore if I have to, but this needs to stop." Compared to the first few books where Harry was like, "we need to go fight monsters", and Ron was like, "Aw fuck, I always get clocked by one of 'em, but lemmee get my coat"; Ron stopped being the "with-you-through-thick-or-thin-guy". In the first book he got himself and Harry dragged into a duel-at-midnight with Draco; on one hand it was a dumb move, but on the other hand, wasn't that literally the first time a peer stood up to a bully for Harry? That's some powerful juju, right there.
It was Ron that stole his dad's flying car to go bust Harry out of Abusive Home Life just based on his gut feeling that Harry needed help. There were a couple times that Harry really needed someone to pull stunts like that ("Listen Harry I maybe kinda...kept Lockhart's wand and I maybe kinda oblivated Umbridge back to primary school with it"), and Ron was totally the guy that was supposed to pull them.
So the Power Trio at the center of the series got unbalanced in the second half because she stopped treating one of them like a protagonist.