"What caught my eye was that it sounded like you were saying that quantum mechanic models are not continuous."
Of course they're not, Jason. Quantum mechanics, like statistical mechanics, describes the behavior of discrete particles.
"I'm not sure what you're referring to because one of the characteristics of wave-functions is that they are continuous and singlevalued."
You're confusing the quantum mechanical wavefunction, which is probabilistic and therefore describes particles in superposition, with classical wave propagation. The latter is the collective motion (consisting of peaks and troughs) of particles though a medium, like water waves. The motion is continuous, but not -- unless the wave is a soliton -- single valued. I think what you mean by single valued is what the conventional interpretation of quantum mechanics calls collapse of the wave function. A continuous wave potential does not collapse -- which is how we get alternative interpretations of quantum mechanics, such as Everett's many-worlds hypothesis.
" . . . the wave-function, which has this peculiar ability to enforce the Pauli Exclusion principle (Hydrogen atom), and interfere with other wave-functions, is nevertheless not any kind of physically tangible substance that we've experienced."
The Pauli Exclusion principle refers to particles, not waves. Waves always interfere with each other; they reinforce and destroy. Statistics governing this kind of motion are called Bose-Einstein, because massless particles (bosons) act as an ensemble -- any number of them can simultaneously occupy the same point in spacetime. Fermion statistics govern discrete particles that have mass (fermions), and the Pauli Exclusion principle is what allows us to tell one from another -- no two fermions can occupy the same state at the same time.
All of this is a part of our physical experience, the continuous wave and the discrete event. The foundational question is that of whether any "tangible substance" exists at all; space and time may be all the substance we need to have mass and energy.
Tom