This is a post I'll continue to add to and revise. These are not films that I recommend, as many of them have questionable material, but they are worthy of interest by filmmakers and scholars, I believe:
The 'body' films of David Cronenberg: Lately he's had a lot to say politically (and his last three are maybe his most mature), but doctrinally his focus on the body should remind us that we don't have all the answers and that there are ways to pose questions in art that are at the very core of our doctrine. What other religion has the ambivalence to the body? We try to forsake the flesh, but also regard it as central to our purpose in becoming like God as well as having families. The flesh is death, but it is also eternal lives. I haven't seen all of Cronenberg's films (his Crash for instance), but I think we should seriously consider them.
Junebug: An homage to Ozu set in the South and filled with religion, but never didactic. We could learn volumes, but it does have some nudity.
Yi Yi: So complex and completely expressive about an entire culture and its relation to the rest of Asia right now. But it is a parable about man's relation with the divine with more than middle-aged maturity.
Me and You and Everyone We Know: There is some sexual content involving people younger than 18, but I wasn't put off by it: it did no glorifying of the sexuality and the view was extremely tender. The film is an affirmation of how fragile relationships are. But the thing that makes me think of LDS filmmakers is how incredibly sincere and complex the characters are. Not only is it an amazing debut film but it is an amazing film. It straddles a line of being an "art film" while being so tender and real at times that I highly doubt it being anything but autobiographical. The film searches for meaning in small things and is concerned with ethics at its core . Unlike so many "indie" sundance-bred pictures, it has more on its mind than just psychology.