Actor Allusion: Taylor makes it quite clear she's attending Yale following high school. Interestingly, Monique Coleman has already attended, and she was even on the paper.
Adored by the Network: Disney Channel (at least in Australia) once had a tendency to overpromote any of the films if it's set to air within a week. Almost every single commercial will have at least one ad about it. Considering that, at least between 2005 - 2010, the film aired once a month, this was quite common.
Since 2015, Disney's main movie channel in Australia tends to play the third film every week, and will commonly play songs from the three films between movies. Descendants pretty much took the trilogy's place on Disney Channel itself.
The Humuhumunukunukuapuaa song and scene were cut from the televised version of High School Musical 2. They reinstated it on the DVD and in the stage adaptation.
There was also a song recorded for the 3rd movie called "Last Chance" that never made it into the movie apart from the reprise in the medley of most of the songs in the movie. A 40 second preview leaked in 2008 before the movie came out.
Dawson Casting: Many of the actors were actually in their early 20s, though when the films initially started, most of the characters were played by people close to their actual age. Taylor's actress, Monique Coleman, was 26 at the time of the first film.
Averted by Austin Butler in the spin-off film, who was nineteen and playing a college freshman.
Though she was raised in Texas and Utah and does not have to fake an accent so this trope is debatable.
Follow the Leader: The success of HSM led to Nickelodeon's blatant ripoff, Spectacular.
Their success likely also paved the way for the similar show Glee, which may have never been picked up without the success of High School Musical, as another musical series - Viva Laughlin - was canceled after two episodes not long before Glee premiered.
Genre Relaunch: Disney's first successful live-action movie musical, discounting productions of old musicals, since Pete's Dragon (1977) killed the genre nearly thirty years prior.
I Want You to Meet an Old Friend of Mine: Prior to the first film, Olesya Rulin (Kelsi) and Lucas Grabeel (Ryan) had been in Halloweentown High together, as Natalie the troll and Ethan the warlock, respectively.
Incestuous Casting: In-Universe. One character remarks that if Sharpay could find a way to play both Romeo and Juliet, Ryan would be out of a job, suggesting that the two have played romantic partners in the past.
Lampshaded in Suite Life of Zack and Cody during the episode "Lip Syncin' in the Rain", where Maddie gets told that she doesn't look like Ashley Tisdale and that she's too nice for the role. She does get the singing role while London lip syncs as her. Chaos ensues.
Romance on the Set: Between Zac Efron and Vanessa Hudgens, who were together for over five years. They confessed to liking each other during the first film and got together during the second. (Although they hid it for as long as they could to avoid media attention). Kenny Ortega admitted that he'd noticed their chemistry since the beginning, and deliberately paired them during auditions.