CONTROVERSY! School me on Tropic Thunder

I'm curious - where does this rate on your Thatz Not Okay scale?

My first take on the movie was that it handled a lot of blatantly terrible things in a really smart way. That Robert Downey Jr's character and Simple Jack are presented as so obviously over the top and wrong, but at the same time it's not a stretch of the imagination at all that someone would do these things seriously. It plays on Hollywood's silly tropes and serious problems alike in a way that makes you see pretty clearly how stupid they are.

BUT, I was uninitiated to Jez and GT when it came out, and as I'm not a member of a group who would be hurt by even a scathing parody of blackface or the "mentally challenged kid with magic power" trope, I feel unqualified to hold this opinion. So school me, what do you think about it?