1. (P & ~Q) is ideally conceivable [can't be ruled out a priori]
2. If (P & ~Q) is ideally conceivable then (P & ~Q) is possible.
3. If (P & ~Q) is possible then physicalism is false.
Therefore, physicalism is false.
(3) is analytic: if you can have P without Q, then P does not suffice for Q, contrary to the physicalist's claims.
(2) is the premise most philosophers [as "type B materialists"] have traditionally questioned. It raises complicated issues in the metaphysics of modality and philosophy of language which I addressed in depth for my ANU honours thesis: 'Modal Rationalism'. (But you can get the short version here.) The upshot is that denying this step is ad hoc and ultimately commits you to the unmotivated claim that there are coherent scenarios which do not correspond to any possible world. I won't address it further here.
The blogospheric discussion has instead focused on premise (1). I think the intuitive force of the premise is made especially vivid by the zombie thought-experiment, whereby we imagine a world physically like ours but lacking in consciousness. That sure seems conceivable, but type-A materialists are committed to denying this, and claiming instead that there is some implicit contradiction which renders the zombie scenario incoherent. Unfortunately, nobody seems to have any idea what this elusive contradiction might be. (Unless you count Eliezer's suggestion, but that was based on a demonstrably false premise in the philosophy of language.)
Brandon made the reasonable point that we're not in a position to assess (1) with total confidence because we don't yet know what the statement P of completed microphysics says. That's a fair point; I certainly don't think this is a knock-down argument. But we do the best we can from our position of uncertainty, and it seems to me that we have more reason to believe (1) than its negation. So we should lean more towards property dualism, pending further evidence.
Some of the other objections that have been raised are, I think, simply confused. For example, Tanasije worries that epiphenomenalists will have no high-level explanation of our 'consciousness'-related behaviour (e.g. my writing this blog post). But we have no fewer resources than the physicalist, we just use different words to describe them. So while I would deny that zombies have beliefs about consciousness, there is a functionalist analogue (or physical component) of belief, which we may call 'z-belief', which can be cited by third parties and will do all the same scientific/explanatory work. (This raises more interesting worries about whether zombie brains are somehow 'malfunctioning' by z-believing in consciousness, which I address in my post: Zombie Rationality.)
Then there's Richard Brown's attempt at constructing an analogous "non-physical zombie" argument (replacing 'P' with 'NP' above) against dualism. But that won't work for the following reason: (i) Either 'NP' explicitly states the qualia facts Q, or it does not. (ii) If it does, then (NP & ~Q) is straightforwardly contradictory, so the first premise fails. (iii) Otherwise, the third premise fails. The possibility of (NP & ~Q) is compatible with dualism, because the dualist never claimed that those other non-physical facts NP suffice for consciousness. So, either way, it's a terrible argument.
As noted in my original post on the current blogospheric dispute, there are some bullets to bite either way.
The [type-A] materialist must simply have faith that there is an implicit contradiction somewhere in the zombie scenario, even though it shows no sign of such incoherence. They must also trust that third-personal scientific inquiry into non-experiential facts will somehow turn out to imply first-personal experiential facts in the same way that it implies the facts about ordinary macro objects like tables and chairs.
The epiphenomenalist, on the other hand, must explain how we can know that we're conscious if it has no causal effect. This will naturally lead to certain views about belief content and epistemology that others might balk at.
I don't think it's obvious how to weigh these various considerations. Personally, I lean towards epiphenomenalism -- the implications don't strike me as particularly worrisome. But your mileage may vary.
[There are also other views [PDF] on the table, e.g. interactionist dualism and panprotopsychism, but I won't address them here.]
P.S. Don't miss the zombie song - 're: your brains' [ht: Chris].