Family-Unfriendly Aesop: "You know, I used to think looks weren't important. But now I think they're more important than anything."
Fanon: According to YouTube comments, Rumbleroar is Aslan's brother. Makes sense. They're both supernatural talking lions who, apparently, reign over their continuities' afterlife.
Fan-Preferred Couple: A very odd case as the show uses the Official Couple from Harry Potter of Harry/Ginny and Ron/Hermione, yet plays out with the creators' own preferred couple of Draco/Hermione. As a result of the show many people who normally did not like the Harry/Ginny ship (mostly Harry/Hermione shippers) have begun to like them in this canon and the (admittedly already popular) Draco/Hermione ship has expanded. But none of these couples take the prize from Voldemort/Quirrel, which has become a major fan ship since this show.
Foe Yay: Malfoy and Hermione. The fact that Malfoy's played by a girl just makes it funnier.
Also, in a limbo-like place, after he dies, Harry asking how Lost ends.
The "Hermione is ugly" Running Gag is this, given that her actor in the films, Emma Watson, is considered one of the prettiest women in Hollywood. (Though she wasn't exactly considered to be ugly when the play was made, either.)
Hollywood Homely: Hermione, intentionally Played for Laughs. She's so ugly that if Draco were to rate her on a scale of one to ten, she'd be an 8.5! 9.8 at the very most. That's why he's holding out for a ten—there's always room for improvement.
Dumbledore: "Severus Snape is one of the kindest, bravest, gentlest, sexiest men I have ever known!"
There are a lot of moments even outside of Dumbledore and Snape, like Neville greeting Harry and Ron with the line, "How are you fine, strapping young gentlemen?" and Harry describing Dumbledore as "the most beautiful wizard". The play is dripping in Ho Yay, probably to make fun of the fan reaction to Rowling's post-series revelation of Dumbledore's homosexuality.
Draco and Goyle have quite a few close moments as well.
Snape smacks Harry on the behind before he does the first task.
Snape: "Is that a new body, my lord? You look absolutely ravishing."
The Scrappy: Bellatrix, if the Youtube comments are to be believed. They might just be envious that the actress got to get... intimate with Joe Walker, the actor playing Voldemort. Die for Our Ship probably has to do with it, too, considering the Quirrelmort relationship is actually what ties the entire play together. Most people claim the reason that she is so disliked is because almost all of the Alternative Character Interpretation is done fantastically but in her case they just made a really cool character annoying. And not to mention that with Voldemort only Affably Evil, she is actually the true villain of the story. Of course, it's not fair to blame the actress and not the writing and directing. The actress actually choreographed the entire show. She also acquits herself nicely in the sequel, where she plays Dean Thomas.
What Do You Mean, It's Not for Kids?: Even less for kids than the later installments of the original series. Once they put it on the Internet and opened it up for all ages, they cut out some of the dirtier portions.
A Very Potter Sequel
Crack Pairing: Draco x Luna, who in the main series never even spoke to each other. Lupin x Cho is also teased- again, never even spoke to one another in the main series (at least not that we know of; he must've taught her class, though).
Not to mention Umbridge and Dumbledore. Or Umbridge and Firenze.
There's even a few references to Snape x Grubbly-Plank, which is so crack filled that more than a few casual Harry Potter fans probably had to do a quick google search to remind themselves who Grubbly-Plank even is.
Crosses the Line Twice: Stomping Scabbers to death after they realize he's Peter Pettigrew, only for it to turn out that Pettigrew was actually hidden in the Taylor Lautner poster.
Any of Draco's monologues about using the potty. They go from amusing to disturbingly awkward to freakin' hilarious.
When Dumbledore rejects Umbridge and she can't stop crying it's a genuinely sad moment. Then Dumbledore assumes she's laughing, starts talking about how funny the story is, and even high fives Snape while she's still sobbing in the foreground. It is hilarious.
Harry Freaking Potter gleefully parodies the Crowd Song chorus:
Harry: But this is all so sad, I mean my mom and dad died long ago...
The song "Home" where Harry talks about never having a home before. It helps that the entire song is sang subdued and softly.
The Mirror of Erised.
Harry and Snape's (temporary) reconciliation.
Harry's speech at the end of AVPS about how Hogwarts will always be there and you can always go back to it. I have something in my eye.
After all the poor Draco goes through, it's nice to see him having a happy ending with Luna.
"The Coolest Girl": an anthem for nerdgirls everywhere.
Future!Draco finally gets to sing a 4-part harmony like he wanted in the first show.
Hilarious in Hindsight: Yaxley as a snivelling coward is made really funny by Peter Mullan's badass take on the character in the first Deathly Hallows film.
Future Malfoy claims that he is very nice and is friends with Harry Potter in the future. By AVPSY, he is nice, and by the end, he does become friends with Harry.
Lucius starts off the play with a line about how there's "literally no way" to continue the storyline, poking fun at how AVPM drew so much of its plot from the final Harry Potter book that Starkids would be forever screwed over in any attempt to produce a sequel (thus making a prequel the only logical choice). Fast forward a few years, and we now have the story of Harry Freaking Potter's senior year.
The scene in which Lucius reveals that he is not Draco's father is meant to parallel a somewhat-climactic scene from Avatar: The Last Airbender between Zuko and his father Ozai. Then we learn that Ozai might not be Zuko's father, either.
Even funnier considering Voldemort said Ozai's speech from the last episode of Avatar word for word in A Very Potter Musicalnote "You're weak, just like the rest of your people ("just like your parents" in Voldemort's case)! They did not deserve to exist in this world — in my world! Prepare to join them. Prepare to die!"
Lucius's declaration that "There is literally no way to move forward from this point!" is surprisingly prophetic in light of Harry Potter and the Cursed Child and its time travel plot.
One of the reasons Ron relates to Spider-Man is that "Iron Man is so mean to him." At the time that line was written, Iron Man had just barely become an A-list superhero due to Iron Man bringing him into the public eye, the Marvel Cinematic Universe was barely a thing, and the idea of that particular Iron Man ever interacting with Spider-Man was believed to be a legal impossibility. Now Spider-Man is part of the MCU and Iron Man isn't remotely mean to him, making the joke seem just odd now.
In-Name-Only: Aside from the Lucius plot and Future!Draco in Act 2, the show is not so much a sequel as a prequel. The only plot that continues onto the sequel because of this is Draco's crush on Hermione.
Lampshaded in the first scene of the first act, with Lucius saying "There is literally no way to move forward from this point!"
Jerkass Woobie: Draco and Snape. Even Umbridge has her moment, after Dumbledore dumps her.
Memetic Mutation: IMA SUCK YOU INTO MY WOMB. AND SPIT YOU OUT AS A RED HOT TITANIUM BABY. WITH DIAMOND TEETH!!
"Did you get my text?" [pause, often the answer, "Yes."] "Well, you didn't text me back."
Agreed, but I think this one deserves special mention:
Harry: I'm not afraid of you! You're a teacher, you can't hurt me. *scoffs* Do your worst.
Umbridge: *turns around slowly* Oh, I will. *CRACK* See you in hell, Harry Potter.
Oh, and don't forget her finger. It bends to an unnatural degree, and it STAYS THAT WAY for the rest of the scene. Unless Joe Walker has double-jointed fingers, that crack probably wasn't his knuckles.
"Guys Like Potter" manages to be incredibly sad despite the use of the word "pwned" and lines like "so many assholes in my face."
Sirius and Harry both seeing James and Lily in the mirror of Erised.
And, at the end of that scene, Snape turning back for a couple of seconds and seeing Lily on her own before the lights fade.
At the beginning of "Those Voices", right when Harry sings "I know you..." That by itself is enough to turn on the waterworks, but immediately after that you can just barely hear a hushed gasp from someone in the audience, which makes the moment even more effective.
The Woobie: Lavender Brown cries when she's scared, so she might qualify.
Draco, who just wants his dad to be proud of him and to use the potty. It doesn't help that Lauren Lopez has some of the saddest puppy-eyes this side of anime.
In a flashback, Dumbledore says to Riddle "Well, Tom... sometimes... sometimes you accidentally kill your family" to cheer him up, referring to Arianna. You can hear the audience go "Hahahaha-ooooohhhhh".
Whatever Filch got up to with a petrified Hermione.
Does This Remind You of Anything?: Done very intentionally in the scenes where Dumbledore talks to Tom about Hogwarts (which is an obvious allegory for a Coming-Out Story) featuring Dumbledore teaching Tom how to use dance as a coping mechanism and features repeated uses of the word 'gay' in its original sense. It's a bit subverted however, as Dumbledore and Tom are canonically gay and bisexual respectively
One-Scene Wonder: Rumbleroar returns for one scene. For some reason, it wasn't shown in the Youtube release.
Also, Tom Riddle's family.
Lily, James, Cedric, Lupin, Sirius, and Snape all show up to sing "Everything Ends" in the Resurrection Stone scene.
Bill, Fleur, Percy, George, the Ghost of Fred, and Mrs. and Mr. Weasley all appear just in the beginning of the show at the Burrow.
Fenrir Grayback and Mad-Eye Moody/Barty Crouch, Jr., appear just in The Teaser.
Special Effect Failure: Darren Criss' microphone malfunctioned and didn't record anything, so all his lines are heard with the camera's on-board mic, resulting in a very distracting shift in audio quality whenever Harry speaks.