(1) It's a minor issue, but Harris's tendency to get sidetracked into polemic repeatedly, and I mean repeatedly, weakens the force of otherwise straightforward argument virtually every time he argues. This is a serious weakness, and it seems clear (e.g., from critical responses to the remarks about Francis Collins in the book) that it makes it harder for critics to take him seriously. And this is a problem. Harris is pretty much the only public New Atheist to have any sense of intellectual strategy worth speaking of; one of his strengths is that he has recognized that a much bolder and more ambitious set of intellectual projects is required if this latest phase of atheism is to end up being anything more than a flash in the pan. Large portions of the intellectual landscape need to be changed. He also, in contrast to, say, Dennett, has a real grasp on the general sort of thing boldness and ambition really entail in this context. What he seems to have difficulty understanding is that this pushes him into the sphere of a different kind of critic, used to heated intellectual debate on precisely these kinds of subject, who find polemic boring, especially if it's polemic against people they don't much think about or care about. They will regard it as so much gab. When you are doing work that is getting the attention of well-established philosophers, the demeanor that avoids unnecessary bias against one's position is that of cool rationality, impervious to anything but argument (unless one can be either viciously witty or can reasonably guarantee that almost everyone is on your side already, neither of which Harris can pull off). And indeed this is what one already finds in reviews of Harris's book. Most of the first third of the article could simply be eliminated -- no one who is going to bother to read Harris's arguments particularly cares about Deepak Chopra's response to Harris, for instance -- perhaps at most reducing it to a sentence or two, and then settling down briskly and quietly to a response to the people he's really decided to respond to, with the paragraph about Colin McGinn. Much smarter way to start.
As it is, however, I would encourage anyone reading Harris just to hop over his polemical passages; his arguments are often stronger than the polemic would lead you to believe.
(2) Harris is entirely right that most of the arguments made against his argument for a science of morality allow for no principled reason not to object to a science of health as well. This is a point that needs to keep being hammered home.
ADDED LATER: I see that Sean Carroll is attempting to address it. Unfortunately, his argument fails, for reasons noted below. (a) The initial values in practical sciences do not require consensus: in order to determine whether there is legitimately a science of health it is irrelevant how many people think health is important, or even what views of health there may be (and there are many more than Carroll suggests). But some of those views of health clearly do allow for scientific study, and thus there are sciences of health. Indeed, to the extent we do agree on health, it's pretty obvious that most of this is due to the science and not prior to it. So the degree of disagreement on the subject is absolutely irrelevant. (b) The initial values in practical sciences identify what is studied; thus removing it from what he calls 'science' is not relevant either. (c) Carroll keeps arguing as if Harris needed to present a complete science of health. I suspect this is because he's a physicist, and so his scientific specialty is one that has had geniuses hammering at it for centuries, ironing out confusions, finding new things to measure, and so forth. But all Harris needs to make his basic case is to present the start of a science, to show that we actually have in hand things that could reasonably be called first steps. Most of Carroll's arguments would, if sound, apply to almost any scientific field in its early stages -- including early physics.
(3) Harris identifies three significant challenges put forward against him; he address the first two at some length and the third, the Measurement Problem, only briefly. The first is the Value Problem:
1. There is no scientific basis to say that we should value well-being, our own or anyone else's. (The Value Problem)
Harris's argument is simply unconvincing on this point, since he concedes too much to his opponents. The fact of the matter is that Harris doesn't have to argue that there is a scientific basis for saying that we should value well-being. Two other positions (not mutually exclusive) are available to him:
(a) There is a basis for saying that human beings in the main do value well-being.
(b) There is a basis for saying that other things human beings value have some real relation to well-being (they presuppose it, or partly constitute it, or some such).
Consider the analogy with medicine again. Suppose you have people who literally do not care about their health in any way, shape, or form. How does that affect medicine? It doesn't. Medicine is a serious field of human endeavor because in the main human beings do value health, and many of the other things human beings value presuppose health. This on its own is enough to get medicine off the ground as a serious field of scientific inquiry, if only it can be established that there are actual scientific methods capable of contributing (however imperfectly at this stage) to our understanding of health. And that, of course, is determined simply by looking at the methods in question. Harris doesn't have to deliver an entire science of morality as a fait accompli; he just has to establish reasons for thinking (1) that it is a worthwhile endeavor; and (2) that at least some parts of it are already feasible. He does want to go farther than that, of course, and not just say (for instance) that only small parts of what we count as morality fall under scientific purview, but he does not have to defend this entire position to deal with the value problem. All sciences having to do with practical matters get their basic values (health in the case of medicine, structural integrity in the case of structural engineering, etc.) from what human beings in fact value. A science of morality need not be any different.
This is, incidentally, a very Humean response to the Value Problem, which is perhaps worth mentioning given that most of Harris's critics deploy loosely Humean objections against his project in general.
(4) The second challenge is what Harris calls the Persuasion Problem.
2. Hence, if someone does not care about well-being, or cares only about his own and not about the well-being of others, there is no way to argue that he is wrong from the point of view of science. (The Persuasion Problem)
This, however, is not an issue arising from Harris's project but a difficulty with theories of morality in general. It's a sensible knave problem. It is true that any theory of morality has to deal with the sensible knave problem, but by the same token Harris can avail himself of any answer to the sensible knave problem that does not rule out the possibility of a science of morality (Hume's own, for instance). Arguably it's a hard problem (which is why rationalists tend to press objections like this against empiricists), but there's nothing about it that makes it a hard problem for Harris in particular.
(5) The Measurement Problem -- that we have no metric for well-being and therefore can have no science of morality -- succombs to similar arguments. For instance, to establish a science of morality Harris doesn't have to establish his full position, nor that he can measure everything to do with well-being; he just has to establish that some things widely recognizable as indicative of well-being or contributing to well-being in some essential way can be. Again, Harris doesn't have to present a fait accompli; he has to present a real beginning.
ADDED LATER (Feb 7): Harris has a new version of the essay up; the same basic argument, but with a much cleaner structure -- the problem noted in (1) is pretty much eliminated, to the great benefit of the argument, and just at a glance (I haven't compared the two side by side) it looks like a few other points might be given somewhat clearer formulation. Say what you will about Harris, but the man learns quickly -- he often revises in exactly the right direction.