Thanks - that does help explain what you meant.

However, I still am not sure what you mean by "mental states" - it almost seems like you are referring to one's specific subjective experience of the outside world (i.e. the answers to questions such as "What does red look like?"), but that doesn't really make sense in the context of the rest of your post. In particular, my confusion derives from statements like this:

My central point is that, even if you were to assemble a complete, accurate model of the brain, right down to every molecule, and program it to carry out the exact same functions that it does in humans, you would not have a full understanding of the conscious experience that model was undergoing.

What I'm getting from it is that you consider questions like "What does red look like?" to have meaningful answers that would prove insightful in understanding the abstract idea of consciousness. But you don't seem to address how such a question would even make sense - that is, why should the color red look like anything in particular? More generally, why would two different people even have the same "experience" of color? All that is true of "color" as a whole is that it is an expression of the wavelength of light entering the eye. Past that it's completely arbitrary. In other words, why would the manner in which one "experiences" color (for lack of a better phrase) have any objective meaning at all?

In fact, in order for such questions to make sense, you would need to first assume the existence of (to pick an example) the color red, no? Because if you don't assume that, then asking how the color red is experienced is itself nonsensical. But you cannot simply assume it either, since if different people "experience" color differently (which they do - again, see synesthesia) then there's no compelling reason to think that there exists some objective "color".

Which I suppose is closer to the heart of my confusion as to your point - the manner in which you talk about "consciousness" seems to at some times take it to be an aggregation of sensory input and at others take it to be some sort of externally observed "state" (once again for lack of a better phrase).

Which brings me to the thought experiment you provided. What I got from it wasn't that it is difficult to define the "mental state" (again, not entirely sure I understand what you mean by "mental states") of a conscious being, but rather that there is no compelling reason to think it is possible to do so. That is, when you look at the color red, the information your brain "stores" is visual input corresponding to a particular frequency of light - when you "experience" the color red, then that is just your brain recognizing that wavelength of light. To be glib, color doesn't exist!

And that brings me to the idea of qualitative experience itself. I'd like to ask you to clarify this statement:

if you want to define a mental state such as pain as this sequence of neural interactions, or as carrying out this particular function, then you need to be able to account for why those interactions, those functions, produce the qualitative experience that they do

Essentially, what I'd like to ask is why it is you would posit the existence of some sort of qualitative experience that is separate from the quantitative patterns of neural interactions - as it stands, I don't see a particularly compelling reason to do so, yet a good portion of what you're saying appears to be predicated on it.