This Reasonable Faith article is worth a read.

First, objective moral values:

So how does Sam Harris propose to solve the “value problem”? The trick he proposes is simply toredefine what he means by “good” and “evil” in nonmoral terms.9 He says we should “define ‘good’ as that which supports [the] well-being” of conscious creatures.”10 He states, “Good and evil need only consist in this: misery versus well-being.”11 Or again: “In speaking of ‘moral truth,’ I am saying that there must be facts regarding human and animal well-being.”12

So, he says, “Questions about values … are really questions about the well-being of conscious creatures.”13 Therefore, he concludes, “It makes no sense … to ask whether maximizing well-being is ‘good’.”14 Why not? Because he’s redefined the word “good” to mean the well-being of conscious creatures. So to ask, “Why is maximizing creatures’ well-being good?” is on his definition the same as asking, “Why does maximizing creatures’ well-being maximize creatures’ well-being?” It is simply a tautology — talking in a circle. Thus, Harris has “solved” his problem simply by redefining his terms. It is mere word play.

Second, objective moral duties:

Does atheism provide a sound foundation for objective moral duties? Duty has to do with moral obligation and prohibition, what I ought or ought not to do. Here reviewers of The Moral Landscape have been merciless in pounding Harris’ attempt to provide a naturalistic account of moral obligation. Two problems stand out.

Natural science tells us only what is, not what ought to be, the case. As philosopher Jerry Fodor has written, “Science is about facts, not norms; it might tell us how we are, but it wouldn’t tell us what is wrong with how we are.”17 In particular it cannot tell us that we have a moral obligation to take actions that are conducive to human flourishing.

[…]Second, “ought” implies “can.” A person is not morally responsible for an action he is unable to avoid. For example, if somebody shoves you into another person, you are not to blame for bumping into this person. You had no choice. But Harris believes that all of our actions are causally determined and that there is no free will.20 Harris rejects not only libertarian accounts of freedom but also compatibilistic accounts of freedom. But if there is no free will, no one is morally responsible for anything. In the end, Harris admits this, though it’s tucked away in his endnotes. Moral responsibility, he says, “is a social construct,” not an objective reality: “in neuroscientific terms no person is more or less responsible than any other” for the actions they perform.21 His thoroughgoing determinism spells the end of any hope or possibility of objective moral duties on his worldview because we have no control over what we do.

If you missed the debate between William Lane  and Sam Harris, here is the video:

And you can read a summary of the debate, written by me. There’s audio in that post, as well.