On the surface Dead Man may seem like pointless weirdness, or in high school terms "super random." And although I find the symbolism loose and confusing, I do think that there is still a very clear message to the work. This is one of many times I have seen the film but i think it made more sense this time because of the work we had done with, Heart of Darkness and Apocalypse now.
Besides all of them having a symbolic river in it (as I cleverly alluded to in the title), these three works have many parallel motifs and they all serve similar purposes as works of art in their respective culture. It was because of the close relationship Dead Man had to more explicit work like Heart of Darkness that I could figure out these Purposes.
All three of these movies form a powerful message on a couple or more different levels. At least two or more levels. One level being sociological or a criticism of actual tangible events in a culture (imperialism, savage wars, western bruteness) and the next a more ontological or 'deep' meaning. It happens that we may be blessed with several 'deep' meanings in each work.
I personally I have noticed allusions to intellectual discovery and universal development as an allegorical theme in each. to be continued for the extra points...