Wow. Tons of great suggestions. Thanks everyone!
I suppose I'll have to go and rewatch AHX. I didn't care for it when I saw it the first time (though Fairuza Balk all dressed up as a byrd was rather nice), as I thought it was a completely inaccurate portrayal of skinheads as well as race relations. It wasn't John Singleton bad ("Higher Learning" is one of the most overcooked dramas I've ever watched in my life), but damn close.
So many good suggestions - makes me want to show clips of them. Birth of a Nation was jokingly suggested, but I think a historical perspective over race in film would be great - I could show the scene of the all-black congress in "Birth," something from "Guess Who's Coming," and continue through the 70's (as bawdy as Mel Brooks' stuff is, he really is using guys in roles that they otherwise wouldn't have been in).
Spike Lee is very good, and I forgot about Bamboozled, which was a phenomenal movie at the time, and now, as a frame through which we can view the Chappelle Show, probably a good selection also.
There's a book on race in film out there called "Screen Saviors," which has some good suggestions, but focuses on the "white savior" character in film, without whom some nonwhite civilization would crumble (Tom Cruise in Last Samurai comes to mind, and what's her name in "Dangerous Minds," as the numerous films of this sort that take place in Africa and the Middle East). It wasn't a very good book, and belabored an obvious point; nevertheless, it was a good resource for choosing movies. Shouldn't have permanently lent out my copy of it.
Thanks again; if anyone has any subtle suggestions (modern movies with poor casting for Asians, confusing Chinese with Japanese with Korean, whites playing as Latinos/Latinas, etc), those are even more fun to use.
As for "defining race," I consider it to be a purely social construction, and one that changes historically, as groups come into social prominence and require a more nuanced view (the variation with which we discuss Muslims and Middle Easterners), and as groups become assimilated into others (why whites no longer express disdain for Irish/Poles/Hungarians/etc to the degree that existed at the beginning of the 20th century).
And since someone mentioned "Black Like Me," I'm wondering if something as absurdly shocking as "Soul Man" would work, because it's both somewhat modern and blatantly racist?