In the Whateley Universe story "Ayla and the Tests", Phase misses several days of school and gets a big lecture in the lab section for Powers Theory class from Dr. Yablonski on Warper powers and warp displacement fields of 'giants' (Warpers who use their power to apparently grow to huge size). In a Lampshade Hanging, Phase even refers to him as Mister Exposition. Guess what Phase faces when they go to Boston? A forty-foot giant who's a warper.
In "Ayla and the Birthday Brawl", Ayla shows (s)he knows too much about taking out mutants with powers, and she talks all about it on the way back from martial arts class. What she says about fighting Package Deal Psychics saves Lancer's life in the big final fight.
Of course, Whatley Academy is a Super Hero School, so it's more than usually justified.
The students at the Hyperion Academy used the information they learned in about electro-magnetism during their weekly physics class to defeat the villainous Lodestone.
Parodied in Friendship is Witchcraft. At the beginning of 'Cute from the Hip', Cheerilee gives a paranoid and seemingly irrelevant lesson about robots and the dangers they pose to society. It's played off as some sort of Freudian justification for why her husband has been distant lately. But then at the end of the episode we're introduced to Sweetie Belle, who is quite obviously a robot. No one notices or remembers the lesson.