Earlier quoted context omitted.
Okay, so, let me try to enumerate these. (1) The hardest part of quantum mechanics to understand is intimately tied to our nature as subjects. Quantum mechanics is an entirely deterministic theory about waves in superpositions which even explains how, why, and when it disappears and averages out into classical probabilities. Except it doesn't tell you why we don't see your television as 50% in your bedroom and 50% in…
Just in case you are serious, or people believe you're serious: 1) Quantum mechanics operates on the quantum level. Macro objects, while composed of countless quantum systems, and thus are the result of the quantum systems of probabilistic particles and waves collapsing and such, are just that: the result of the quantum systems. This isn't subjective experience; it's an underlying behavior baring forth a different le…
But the quantum behavior does really matter. The clean part of QM says that if there's an accumulation of events which would transfer my TV into my bedroom with probability 50%, my TV is described by the state matrix ½ |L> is its state in my bedroom and |L> is its state in my living room.
But we don't see that state. We see |L> or we see |B>. That is the "hardest part" of quantum mechanics, where one insists that the above superposition describes many worlds or that there is a nonunitary wavefunction collapse or whatever.
(2) I don't require that the brain change the laws of physics or decide that certain waveforms collapse in any particular way. However, for reference, quantum mechanics does work that way, so get used to it. A system "over here" can indeed "decide" how a system "over there" will collapse.
If I have photons over here in a fiber-optic cable, I can perform a measurement which will change the result of a double-slit experiment over there. I can choose whether the people over there will see an interference pattern or not. In fact, I can choose whether it will happen after their detectors have already measured their photons. We've done this experiment, it has been confirmed, and if it weren't confirmed, QM would just be flat out wrong. [Theory details: start with (|00> + |11>) ⊗ (|0> + |1>), apply a CNOT from qubit 3 to qubit 2, then choose to measure qubit 1 in either the |0>, |1> basis or the |0> + |1>, |0> − |1> basis to destroy or restore the interference pattern at qubit 3. It's called a "delayed-choice quantum eraser."]
We gave up that very sentence, "if one develops an accurate enough model of the universe, the base stuff it's made of, you can predict the future", with the advent of quantum mechanics -- at least, in the way I think you intend it. Hey, here's a nice quantum system, it's in the state |0> + |1>. You measure it in the computational basis. No matter how accurate your model is, you cannot predict which one comes out. If you could, you could do experiments to prove that nature was self-contradictory.
(3) The problem is precisely that the "results of the conscious process" don't appear to be mechanical, such that we can't empathize with machines. It's not just "we don't," but that machines are so precisely understood, and so simple, that you would have to invent a "ghost in the machine" and believe in weird supernatural crap to have them really feel anything. Hell, you probably think, for all your talk of rationality, that I really believe in ghosts -- and it's for precisely this reason. Machines seem to require a "ghost" inside them to feel.
What I want to say is different. If this supposition is correct, then applying it back to our own case poses a trilemma. Either (a) we don't really feel anything, or (b) we are not machines, or (c) we're stuck with weird supernatural crap. Of these three, (b) is the "easy way out;" abandon functionalism. It comes with its own problems about what we replace it with; functionalism is not easily replaced. There is an alternative (d) which is to not take the problem seriously, which many influential philosophers including Dan Dennett have made a reasonable option, but it seems unsatisfyingly to fall into the attitudes of (a) and (c) when actually practised.
(4) Quantum systems sometimes form higher-order excitations which escape the parallel and the serial. Electrons in parallel only flow with resistance. Electrons in series also only flow with resistance. A Cooper pair is a two-electron excitation which flows without resistance, even though its constituent electrons could only flow with resistance. It requires a higher-order description. That is very rare in mechanics.
(5) Take it one step further: classically, you aren't even the pattern of atoms that comprise you. That's what the Star Trek example proves. We could create two copies of this pattern classically, and there would suddenly be two distinct people in the universe. If someone pointed a gun at you and said, "hey, we've got to kill you, we created this identical doppelganger of you down on the planet, and now we're convinced that he's the real you," that would seem awfully disturbing to anyone. The only reason they go along with it in Star Trek is because we kill them before they can react.
But quantum mechanics offers something fundamentally different. You could be the quantum pattern. Or, at least, the Star Trek thought experiment wouldn't suffice to disprove it. That's why one might be hopeful that there is something quantum about mind.