Parallels to Batman
One of the things I thought was really impressive about Joker is some of the parallels drawn to Batman himself.
1. The faux-connection to Thomas Wayne. Even though it turns out to be false, the idea is still put into our heads that the Joker has the same origin as Batman. This is reinforced by his imaginary appearance on Murray's show, talking about his lack of father.
2. Joker starts as mysterious figure, mentioned in the papers, a man who wears a mask and hurts menaces to society. Instead of criminals, they're yuppie creeps, and instead of a man in search of justice, he's a scared guy with a gun. But the parallel is there.
3. The populace takes up Joker as a symbol - a hero - for their struggles.
4. Joker fully dons his mask and takes up his mantle.
The film draws twisted parallels to Batman. We could read this as being a dark mirror of the Dark Knight, but it could also read as a critique. Who is Batman? He's a criminal. He's outside the law. He beats down people (like Arthur) who are just tired of being ignored. Maybe he's doing some kind of right, some kind of good, but...
Well...it's what makes us laugh. It's all subjective, isn't it...?
That, the political angles, the character study...this is a well-layered movie.