Voldemort's pre-Avada Kedavra speech to Harry is straight from the finale of Avatar: The Last Airbender. Ironically, this seems to be the one dramatic moment the audience doesn't reflexively laugh at.
Ginny tells Harry, "We kissed at the Yule Ball, and, well, I thought we were going to be together forever.... but we're not." This is almost identical to what Aang says to Katara in The Ember Island Players (though he refers to the invasion of the Fire Nation).
And the scene when Ron and Hermione first kiss is the scene between Aang and Katara before the fire nation invasion where Aang kisses Katara. The dialogue leading up to the kiss is almost identical.
Voldemort (in the Zefron poster) shouts "You gotta get'cha head in the game, Weasley!" which is a reference to a High School Musical song, "Getcha Head In the Game". And no, I am not ashamed to know that.
"How many times do I have to kill you, boy?" from their second confrontation is a direct quote from Aladdin.
When Harry and Ginny are dancing they quote from Anastasia, "We've stopped spinning."
"You came back?!" "I came home!" is a quote from Tarzan, though it's used even more dramatically here.
Dumbledore's description of what would happen if Harry didn't compete in the tournament, and Hermione's reaction — "Total protonic reversal!" — is a Ghostbusters reference.
Goyle seems to be channeling Ogre when growling "NERDS!"
Draco's rolling around on the floor could be seen as a reference to Fitzwilliam from The Big Gay Sketch Show, also an English schoolboy (and coincidentally also played by a girl).
It's more of a Shout-Out to the way Tobias from Arrested Development always rolls around when he messes up a pose and tries to make it look like intentional.
One Death Eater's nickname for Dumbledore is Bumblesnore, which sounds suspiciously like "Bulbasaur".
Harry and Ginny's and Ron and Hermione's in AVPS romance is compared to Spider-Man and Mary Jane.
The guitar intro to "Granger Danger" is exactly the same as the intro to the Suzanne Vega song "Marlene on the Wall".
Several times, you can hear lines sung to tunes from Wicked. "Different As Can Be" gives us the lines "We share some hands and fingers" "and yet, the feeling lingers" lines sound very much like part of "What Is This Feeling". Arguably, even, Voldemort and Quirrell could be seen as Elphaba and G(a)linda. "To Dance Again" gives us the line "And when I'd start to sway/I'd get carried away", which is a near quote from "Wonderful".
The melody of "To Dance Again" is also identical in tune to "Wonderful" at the beginning of their chorus part.
Wizard of Oz: Won-derful.
Voldy: To dance agaaaaaiiiiin.
Hermione does the same awkward, out-of-sync dance as Elphaba. She even waves her arms the same way.
"Never tell a girl you like her, it makes you look like an idiot" could be a reference to line by Daniel Desario in an episode of Freaks and Geeks.
When Cedric is introduced he pushes the Trio+Ginny to the floor, parodying the scene in Goblet of Fire where Harry, Ron, Hermione and Ginny crash to the ground after using the portkey and Cedric lands perfectly like the perfect Mr. Perfect he is.
When teaching the students about Patronuses, Lupin tells the children that they need a happy thought, which they reply in unison "Any happy little thought?"
In the same scene, Lupin complains that the DADA textbooks are so old, they still refer to "Dementors" as "Ring Wraiths".
Lupin lists the rival houses for Gryffindor: Slytherin, Ravenclaw and Jigglypuff.
Avatar: The Last Airbender: Lucius telling his son that banishment was too merciful (Day of Black Sun Part 2) and Hermione telling Draco that she can't forgive past him but can forgive future him (The Southern Raiders).
"That's rough, buddy."
"Get those happy thoughts ready and don't cross the streams!" is another Ghostbusters reference.
Ron and Harry's first Red Vines conversation, which cements them as best friends, is a riff on a conversation with the exact same structure and purpose of bonding in Step Brothers. The variation is that here, each question has the same answer.
The running joke of Lupin and Sirius sniping over who really was James's best friend seems reminiscent of Barney and Marshall doing the same thing (over who is Ted's best friend) on How I Met Your Mother.
In "Harry Freakin' Potter," when the cast sings the word "superstar," they all fall to one knee and throw the peace sign in the air with both hands, much like Mary Katherine Gallagher.
One from the other musical Team StarKid did, Me and My Dick, when at the end Sirius says he's always wanted to see Venice, just like The Old Snatch, the character Nicholas Joseph Strauss-Matathia played in the other musical.
Also: The pizza box with a hole in it? Anyone else getting MAMD Flashbacks?
The paintings on the third floor. "The dogs playing poker peed on the carpet! The screaming man has never looked so terrified! It took the entire last supper to calm him down!"
Also, am I the only one who thinks that the scenes where Lupin walks around naked is a Take That to Twilight? The werewolves in Twilight are hunky, muscular Native Americans who often go shirtless. While Lupin isn't ugly in the slightest, he's very pale, only wears tighty-whiteys after transforming back into a human, coated in blood after said transformation, and he does humiliating things while naked. If that isn't a Take That, I don't know what is.
Possibly a coincidence, but the central plot is rather similar to the 2009 Star Trek film. A villain who has lost everything travels back in time with his followers to when the heroes first met, planning to exact revenge. Meanwhile, one of the good guys, who is the hero's enemy in the past, travels back as well and helps thwart the bad guy.
When Harry says that "you can't have more than two friends", it's very similar to a line said used Sam Weir to justify not wanting to be friends with Cindy after she initially appears to reject him.
Lupin says that the way to achieve a Patronus is to think a happy thought, to which the kids respond in unison, "Any happy little thought?"
Arthur Weasley at calls non-magical people Moogles.
Neville claims the doe Lupin killed was Bambi's mom.
Back to the Disney themes: While Lucius Malfoy reveals Draco's true parentage he claims, that 'now he will do what he should've done 12 years ago' which reminds me of one judge Frollo from 'Hunchback of Notre Dame'. Also, in 'No way' there's this line 'break out your mad eyes—' which reminds me of this scene  Toy Story 2. Not sure if it's intentional though...