Yes, quantum theory is a theory of waves.
OldPilot said, "QM uses the concept of a 'de Broglie' wave for a particle."
That's a name that probably has not been heard outside of high-school physics books for something close to a century. It's true that Louis DeBroglie's theory was the first in a string of ideas that eventually led to the formulation of modern quantum field theory, but the fact that you say, "de Broglie wave" is telling.
"...the 'Dirty Little Secret' of Theoretical Physics: We have NOT yet figured everything out."
Well Yeah! What do scientists do for a living? They try to figure stuff out. The day when everything has been figured out is the day when the last scientist cleans out his desk and goes home.
"The universe is governed by whole sets of 'Laws'..."
No. The universe is not governed by our laws. A scientific law is a formal (mathematical) description of some pattern or phenomenon or behavior that, as far as we know or as far as we have observed, is always the same. We make the laws to fit what we see. It doesn't work the other way 'round.
"...that do NOT agree and are mutually exclusive..."
In order for something to be called a 'Law' it *MUST* agree with nature. It is simply not possible for two scientific laws to disagree with one another, because they both must agree with reality. I think that you are confusing 'Law' (see above) with 'Theory.'
Scientific theories can be, and often are, incompatible with one another. The best example probably is the clash between general relativity and quantum field theory. The laws of gravity (as predicted by general relativity) agree with everything we have observed about gravity. The laws of particle physics (as predicted by quantum field theory) agree with everything we have observed about certain other forces (e.g., electromagnetism). Physicists would like to believe that some common structure underlies both gravity and electromagnetism. Unfortunately, the mathematical structure of QFT is deeply incompatible with the structure of GR.
If a common theory ever is found, then it will invalidate either QFT, or GR, or both, but it will not invalidate the laws (i.e., the patterns and behaviors and phenomena that we have actually observed in nature.)
"...2 slit experiment...explain how a particle orders of magnitude smaller than the distance between the slits somehow...interferes with itself. Problem, we cannot explain this well using 'quanta' (Particles, photons). Wave mechanics gives a simple easy to understand explanation."
You misunderstand the meaning of the word "Quantum." Quantum theories are WAVE theories. Things are quantized because of the fundamental, inevitable ways in which standing waves behave. That's what set de Broglie off in the first place. His peers were observing energy levels that were quantized, and everyone was trying to figure out how could that be? De Broglie's insight was that the energy levels of a standing wave were quantized, and so he proposed that maybe the energies were quantized because the so-called "particles" were, in actuality, standing waves.
"What to do? We cheat! We say that electromagnetic radiation has a dual nature..."
The authors who write pop-science books still say that. Physicists don't---not anymore. (see below)
"Quantum Mechanics gets out of this mess by introducing the Uncertainty Principle, Indeterminacy, and the Copenhagen Interpretation of QM."
The so-called copenhagen interpretation is one of about six different approaches to what is known as the "measurement problem." It is still considered to be main-stream, but the number of adherents is dwindling. Copenhagen believers say that the waves in quantum theory are not the reality, but rather, that they merely represent what the experimenter KNOWS about the reality. The problem with this viewpoint is that it fails to explain how it is that our knowledge can be so precisely constrained by wave mechanics if the waves are not somehow 'real.'
In all of the other main interpretations, the waves are indeed considered to be part or all of the reality. A growing number of physicists however are beginning to back off from trying to understand what QFT actually MEANS, and they just say, "It works as far as it goes, but we've still got a lot to learn."
That 'dirty little secret' is not as secret as you think.