The fact that it could be difficult or impossible to know exactly how to maximize human wellbeing, does not mean that there are no right or wrong ways to do this — nor does it mean that we cannot exclude certain answers as obviously bad. The fact that it might be difficult to decide exactly how to balance individual rights against collective good, or that there might be a thousand equivalent ways of doing this, does not mean that we must hesitate to condemn the morality of the Taliban, or the Nazis, or the Ku Klux Klan — not just personally, but from the point of view of science. As I said at TED, the moment we admit that there is anything to know about human wellbeing, we must admit that certain individuals or cultures might not know it.
I agree with his last sentence, and also that once we've solved the philosophical problem of what human well-being consists in, it's an empirical question what are more or less effective means to this end. But Harris' claiming the mantle of science for his fundamental values is just so much empty rhetoric. Sean Carroll is exactly right to point out that there's no empirical experiment you can run to decide what ends are worth aiming at. In his response, though he seems not to realize it, Harris is effectively just assuming that the collective good (i.e. 'maximizing human wellbeing') is what fundamentally matters. The only role he sees for individual rights is instrumental, not foundational. Now, I happen to agree with this view, but it must be acknowledged as a controversial moral claim that needs to be defended on its merits, and not merely assumed. (And again, it's clearly not a question of empirical science.)
So, does Harris say anything to defend his preferred ultimate values? A little, though it's difficult to assess because he's not sufficiently clear about what his view actually is, and what he means to be ruling out. In any case, the core of Harris' positive argument seems to be as follows:
I believe that we can know, through reason alone, that consciousness is the only intelligible domain of value. What’s the alternative? Imagine some genius comes forward and says, “I have found a source of value/morality that has absolutely nothing to do with the (actual or potential) experience of conscious beings.” Take a moment to think about what this claim actually means. Here’s the problem: whatever this person has found cannot, by definition, be of interest to anyone (in this life or in any other). Put this thing in a box, and what you have in that box is — again, by definition — the least interesting thing in the universe.
This seems to rest on a similar confusion to that which I warn against in my old post, Confusing Welfare and Happiness. Distinguish two senses of 'interest': (i) the descriptive matter of what someone is interested in; and (ii) the normative matter of what someone has reason to care about, or what they ought to be interested in. Harris seems to be conflating these two. Just because nobody is actually interested in some X, it doesn't follow (let alone "by definition") that nobody ought to be interested.
Perhaps Harris could respond by shifting the goalposts, and suggesting that anything we could care about ipso facto counts as having 'something to do with the potential experiences of conscious beings.' But then his criterion is trivialized, for I don't see that he's made any argument to suggest that there are principled limits on what conscious beings could potentially care about. Note, in particular, that we are entirely capable of caring about things other than our conscious experiences. This completely undermines Harris' apparent identification of 'wellbeing' with 'felt happiness'. Insofar as he means to be ruling out any rival views in claiming that "consciousness is the only intelligible domain of value", his argument rests on a sleight of hand.
Now, I don't think this is any cause for despair. The failure of such over-ambitious formalistic arguments merely shows that we can't give formal proofs for our normative views. But that should come as no great surprise, and it certainly doesn't mean that we must forsake rational inquiry altogether. It remains open to us to engage in the process of wide reflective equilibrium: considering our conflicting judgments about various cases and general principles, and searching for the most plausible ways to resolve any inconsistencies we may find in our moral thought. (In particular, we can argue against various forms of relativism and religious ethics on grounds of their substantive implausibility.) There's no guarantee that this process will lead us, or others, to truth -- it's always possible to be incurably crazy/misguided, after all, as Harris is well aware -- but it's the best hope we've got.