Besides the term Ubermensch, the other saying which Nietzsche is famous for is "God is dead." Meaning of course that humanity has moved beyond its need for religion- and God- as a foundation for society. But what, Nietzche then ponders, will fill this void? Simple: man will become his own god... “Is not the greatness of this deed too great for us? Must we ourselves not become gods simply to appear worthy of it?” The Ubermensch will determine for himself what values and ideals should be pursued. Rope definitely references this concept in Cadell's outraged refutation of it near the end of the film, "Did you think you were God, Brandon?!"
Nietzsche criticizes Christianity for inventing the concept of sin as a method of manipulating people into repressing certain natural drives or desires through guilt and fear. Whereas he believes that no human impulse or urge is negative, to be suppressed or hidden, but rather these can and should be mastered and honed to serve a useful purpose: The church combats the passions by cutting them off in every sense: its technique, its ‘cure’ is castration. It never asks: ‘how can a desire be spiritualized, beautified, deified?’ Obviously, as a Christian, I think Nietzsche is full of crap; anyone who thinks that man will throw off the traditional- and Christianity based- morality which underpins western society and become a better, more advanced people is either touchingly naive about human nature, stultifyingly stupid, or willfully blind... maybe all three in combination. Greater thinkers than I have definitely thought so as well; some time ago I posted about an essay by GK Chesterton (link below) which contains a thorough debunking of Nietzsche's Master/Slave Morality philosophy (strength is right/moral, weakness is wrong/immoral). Though of course some people have found his philosophies to be quite useful in pursuing their own nefarious ends- most notoriously Hitler, who grasped Nietzsche's Ubermensch ideal with both hands and enthusiastically ran with it... turns out that it wasn't much of a leap from Master Morality to Master Race. Go figure.
When Cadell opens the chest, we don't see David's body: rather, the camera focusses on Rupert's face; there is horror in it definitely, but also shame. He is not responsible for the murder, obviously, but for the first time he sees the philosophies which he's prated about his entire adult life for what they are- where they can lead, and what they can lead to. He realizes that the ideas that he so smugly and cavalierly espoused and championed in theory are repugnant and yes, immoral in practice. This really struck a note with me, because how often we see this in real life: self-satisfied elitists who preach policies and systems which they have no actual experience of, and which spell disaster for anyone who does (socialism, anyone?).
So those are my thoughts on Rope... not a perfect movie by any stretch, but I really enjoy the interactions between the three main characters- especially in the last part of the film- and the critical eye turned on Nietzschean philosophy.