What all information can be gathered qualitatively from the radial distribution functions of a molecule?
You can get alot from the RDF... an amazing amount actually. It is true though that people like printing out the RDF and thinking their paper now has substance, but there is so much more to the pair correlation function.

Integral equations are based on g(r). Kirkwood-Buff solution theory is too. Kirkwood-Buff solution theory will make you dizzy with what it can calculate.

See wikipedia for more on Kirkwood-Buff solution theory. See Arieh Ben-Naim's Molecular Theory of Solutions for the real deal explanation. What a good read. I get excited everytime I get to link it. Ben-Naim, amazing book