Just a few rough ideas off the top of my head that could be honed if anyone's interested:
Treatment of Christianity--positive or negative? how so? explain.
Racism in Ethan Edwards--how do we resolve it, or do we?
Fair fights--Martin v. Charlie--and "manly" behavior
Evolution of female characters in Westerns--can we get to the "truth" about frontier women or are we always invested in the cultural expectations of those writing the history?
Cultural identity: inborn or acquired? (What do you make of Ethan scalping Scar???)
Ties to Western tradition (dime novels, radio, TV, etc)--trace the evolution of an idea you see carried from one text to another.
Intelligence/Education/Literacy--how important is it in a man in the West? The suitors both seem less intelligent than Laurie Jorgensen--just as her mother seems more intelligent than her husband. Why? (What is the purpose of marriage in this setting?)
What cultures mix and which are excluded? (Mexican, Norwegian, Confederate, Commanche... and what happens to those of mixed race?)
Scar, the blue-eyed Commanche (HUH???)--connection with Alexie's essay "I Always Hated Tonto"?
The impact of The Searchers on future films and why this relationship is important to recognize
Hero: which character is the hero? why? what are the pros and cons of each option we're offered? why this cast of such problematic heroes?