Next I will violate the directive not to address Harris's "peripheral" arguments or his claims made in other writings. These include claims that it is not "decent" for individual Muslims to build community centers too close to a historical site of terrorism led by other individual Muslims, that 'we' should profile Muslims, that the War on Terror should be considered instead a War with Islam, and that it is either legitimate or regrettably unavoidable for those prosecuting the War on Islam to employ torture--and to generally renounce scruples. Harris also claims that the U.S. would face a moral quandary if an "Islamist regime" ever obtained long-range nuclear weaponry: a pre-emptive nuclear strike against the country living under that regime would be an "unthinkable crime", but, regrettably, it may be "the only thing likely to ensure our survival."
I infer from these claims that Harris believes that the violence and atrocities committed by Muslims signal something irreparably wrong with all of Muslim civilization, whereas even greater violence and atrocities committed by non-Muslim Americans (including elected ones like Dick Cheney) are not nearly as tainting of American civilization. Harris is also willing to morally consider, on a utilitarian or survivalist basis, military actions by the U.S. that will regrettably lead to mass torture and murder of vast numbers of noncombatant Muslims. I doubt, however, that he would ponder long before condemning without reservation military actions by Muslim nations that would lead to the torture or murder of a single noncombatant Judeo-Christian American. Harris's moral attitude towards Muslims may thus be summed up as, "It is okay--even imperative--to do to Muslims what we would not have them do to us".
Now I need only demonstrate, with cogent reference to empirical evidence (facts), the incorrectness of this moral attitude towards Muslims (values). Such a demonstration would pit Harris's commitment to his central thesis against his commitment to this attitude. Then, to the extent Harris identifies more with the latter (and I suspect he does), he would have some reason to discredit his own Moral Landscape thesis to reduce dissonance.
That is, if Harris rejects the notion of moral laws that can be objectively and universally established, then he could consider himself as entitled to his Islam-hating orientation and related endorsements of atrocity as honor-killers and wife-stoners are entitled to theirs. Though Harris may resist this relativistic view now, plausibly "scientific" evidence that his values are wrong may inspire skepticism that scientific evidence can ever speak non-tendentiously to the question of what values are wrong.
It is indeed daunting to identify a non-tendentious objective standard for judging right and wrong. I will therefore appeal to Harris's affection for psychologist Steven Pinker, whose positive review of The Moral Landscape is proudly excerpted on its back cover. One of Pinker's more provocative theoretical innovations is to ground the normative appeal of the "Golden Rule"--do to others you would have them do to you--in the empirical evidence of psychological science rather than in the pronouncements of religious authorities.
Pinker, in Better Angels of Our Nature , notes that the empirically well-established Flynn Effect--a longitudinal finding that the intelligence required to attain an "average" score on IQ tests has increased over time--is driven primarily by advances in abstract intelligence (rather than in, say, writing ability). Pinker sees this fact as explaining, to some extent, worldwide declines in violence--an obvious moral good. Pinker argues that the rise in abstract intelligence may have contributed to increased peace by increasing our tendency to follow the abstract moral algebra of the Golden Rule (as opposed to more particularist moral pronouncements like "Thou shalt not lie with man as with woman", "Thou shalt not eat shellfish", etc.).
The Golden Rule's algebra appears simple: If you oppose having Z X Y, then Y should not X Z either (with Z being "others", Y being "you", and X being actions like "kill, oppress, torture, colonize, steal land from, bulldoze homes of, discriminate against on the basis of creed or culture, and drop nukes on"). Following the rule is actually quite difficult, though, because heuristics, self-justification processes and rank hypocrisy play such an outsized role in human psychology. Still, according to Pinker, cultures attaining more advanced abstract intelligence can guide themselves more reliably with this rule across various domains. Pinker also argues that the lower IQ scores of past generations (suggesting a "retarded" average a century ago) can be explained primarily in terms of moral retardation.