I'll whittle away at that question bit by bit.
First, we don't have to worry about the Newtonian picture. It's now explicitly just an approximate description which resembles the more fundamental descriptions within a certain range of parameters.
Now we have to reconcile GR and QM, each of which takes the form of a nominally universal theory. First, let me touch up your descriptions of them. GR doesn't have energy flowing in a fixed geometry, but rather a coupled behavior of the geometry and the energy flow in it. QM is not really more discrete than classical pictures. The fundamental dynamics are intrinsically continuous, as in Schroedinger's equation.
So what's the issue between GR and QM? QM provides an acceptable version of other fields (e.g. electromagnetism) even though their behavior on large scales is more typically described in classical language.Why is gravity a problem? The issue turns out to be technical, and somewhat over my head.
If you start with a simple process, QM intrinsically dresses it up with fluctuations around the nominal average value. These fluctuations are then dressed up with further fluctuations, etc. You can see that there's a danger that if you keep carrying this procedure out the physical results may not converge to any finite number. For the other physical fields (the electroweak field and the QCD field) it turns out possible to formulate things so the answers to physical questions from this infinite series come out finite and correct. For gravity in standard 4-d space., that isn't possible, again for specific technical reasons connected with the spin-2 property of the graviton. Thus in a standard 4-d space, there doesn't seem to be a way to have everything described by QM and still have gravity present. If you try to limit the applicability of QM to only some forces, then serious logical problems develop. However, the string theorists tell us that in spaces with 9 or 10 spatial dimensions (depending on the ingredients of the theory), well-behaved quantum theories are possible which include effects equivalent to gravity.
(published on 08/10/09)