I'm not sure if it quite counts as satire, but The King of Comedy is an perplexing movie about a man's obsession with a talk-show host. I watched it a couple years ago and sat through the credits unsure whether or not I loved or outright hated it for toying with my emotions so much. (Oh, and it's a Scorsese movie starring De Niro, for what that's worth)
I remember seeing a Scorsese quote saying he felt it was the movie of his in which De Niro performs best. It's also a great movie that stands out from Scorsese's typical style. When I was a "film buff" in high school (haha) it was my favorite movie by him next to the aviator or Alice doesn't live here anymore.
I put it in the same box as Match Point: a great watch, but also incredibly frustrating. I had to actively subdue my urge to yell at the screen in order to enjoy the movie. I think by kleinbl00's standards, it doesn't fit the genre of satire, but I would wholely recommend it to people to watch outside of #movieclub