When Dumbledore says Hogwarts has a "hidden swimming pool", he's not kidding. Harry visits the "hidden swimming pool" (or giant bathtub, either one) in the prefects' bathroom in the fourth book.
Snape shows Harry exactly what he needs to do. Die, of course!
Bellatrix tells Voldemort there are "pieces of [him] missing", and Voldemort defensively asks if she's talking about his Horcruxes. Considering how Voldemort survives, she is talking about one of them.
In Ron's first year he was told he doesn't get the girl by future!Draco. So he's a bit of a butthead — he's protecting himself by denying any feelings for Hermione until Granger Danger strikes and he can't deny anymore.
This fits with how in AVPSY, where they are together, he's no longer mean to her at all (not counting his "affair" with Lavender.)
Hermione honestly doesn't seem to care that much when Draco rates her 9.8/10, but that makes sense when you realize that she's known about Draco's crush on her since her first year.
In the books, Quirrell really is the only one of Voldemort's followers who refer to him by that name (though this is probably a case of Early Installment Weirdness).
Cho Chang is white, not Asian as one would expect. It's funny enough on its own but becomes even funnier when you realize that this isn't technically a contradiction of the source material. At no point in any of the books is Cho explicitly said to be Asian! You just assumed because of her name! RACIST SISTER!!!
There are a few clues that Scabbers isn't Peter Pettigrew. First Ron mentions that his parents found Scabbers the same night that Harry's parents died. In the books, it was a few days before Sirius caught up to him and was framed. Second, Sirius used the Invisibility Cloak to escape Azkaban (somehow) instead of escaping as a dog, suggesting that the Marauders didn't become Animagi.
When the kids save Sirius by casting the Patronus Charm, we see four patronuses, even though there are five people (Harry, Ron, Hermione, Draco, and Yaxley). Yaxley most likely did not cast the spell, because Death Eaters can't produce a patronus.
"Guys Like Potter" is Lucius trying to emotionally manipulate Snape into helping him (or at least not ratting him out) by convincing him that the only way to stop nice girls like Lily falling for assholes is to eliminate the assholes. But for someone who is coldly manipulating Snape, Lucius sure puts a lot of emotion into it. And although sometimes in the song he addresses Snape directly, at other times he uses "we" and seems to identify with Snape ("We'd treat them nice and never be mean/and we would care..."). It all made sense for this troper once I realised that Narcissa cheated on Lucius with Dobby, and Lucius' hatred of Draco is actually pretty similar in origin to Snape's loathing of Harry: he sees the father in the son, and is constantly reminded of losing the love of his dream girl. So he actually does genuinely identify with Snape!
According to J.K. Rowling, Harry Potter and the Chamber of Secrets was originally going to be called Harry Potter and the Half-Blood Prince. This eventually became the title of the sixth book, which also contained some of the plot points that originally was a part of the second book. This play contains elements from both of these books. It also implies that the Harry Potter books were originally written by Hermione as a presumably truthful account of Musical Harry's adventures, meaning that it too would be a mix of the second and sixth books. Her essays were then heavily edited by Gilderoy Lockhart, who dramatically changed the order of which the events unfolded, creating our universe's Potter books while splitting up the plot of AVPSY into two separate stories.
Once when discussing Gilderoy Lockhart, J.K. Rowling speculates that he would take credit of writing the books if he could. In AVPSY, that's exactly what he does.
Why is Diary!Voldemort more of a villain than in the first play? Quirrel and Normal!Voldemort had spent a lot of time with Quirrel and probably got influenced by him, becoming Affably Evil. Diary!Voldemort didn't. And at the end he himself says Harry Potter taught him how to love. Diary!Voldemort is more evil because he's just a memory of Voldemort before this
If one interprets Quirrell's love saving Voldemort as Quirrell literally being a horcrux. That means that it would be literally impossible for Voldemort to die unless Quirrell does. Sounds kinda awesome, right? But if one mistakenly believed that Voldemort was still evil and needed to kill him, they would first need to murder the first and only person that Voldemort ever felt a shred of compassion or friendship towards