Just watching this movie now for the first time, and it strikes me...this could be an unofficial prequel to The Dark Knight, about The Joker before he goes insane. Because Heath Ledger's character looks like this, he's already rumoured to be a lawbreaker, is a smartass, handles a knife pretty well in one scene, and can organise elaborate attention grabbing schemes like this:
(which illustrates he also has experience talking to people over a speaker, and evading cops). There's also a bunch of rumours about him selling his liver, and eating a live duck, which is kinda like a goofier version of "You wanna know how I got these scars?". And to top it all off, his hair gets painted green in one scene! PLUS, Joseph Gordon Levitt is also in this movie, and he was in Inception, so maybe Christopher Nolan is a fan, got some of his actors from it, and intentionally wrote the Joker to fit in with 10 Things I Hate About You? EH?