Let me step into the firing line, gents, by saying I largely agree with LY, though I would've put it differently.
There is an article linked to by sunyavadin that does a good job of critiquing new atheism and Harris in particular.
His anti-Islamism seems to have a blind spot for most of history when Muslims were more tolerant and more developed in science, arts and medicine than Christians. He may stroke our ego by juxtaposing a Tibetan monk who after years of torture was only afraid to lose compassion for his captors and what he perceived as the attitude of hate and intolerance of Islam (linked at the bottom), forgetting people like Badshah Khan , forgetting that the most populous Muslim country in the world right now is a pluralistic democracy with transgender TV personality, freedom of religion and press. Ignoring the massacres of Tamils by Sri Lankan Buddhists, forgetting the massacre of Bosnian Muslims by Serbian Christians, forgetting the genocide of Circassians by Russian Christians, forgetting the genocide of Dzungar musilms by Chinese Buddhists, forgetting the Japanese Buddhist teachers encouraging the war... And of course he ignores the fact that the top three of the worst atrocities of the past century were orchestrated by atheists - Nazis, Communists and the Khmer Rouge with science and technology enabling the scale of devastation and loss of life never seen before.
Looking at the intolerance in his own backyard, it is easy to see how the hermeneutics of religion, rather than the literal texts, play the most significant role. I mean the context, the interpretation, the reality on the ground, so to speak, which can vary widely for the same religion. Look at the variety of religious expression of every religion. It was the Buddhists as kamikaze who pioneered suicide attacks, Hindus as Tamil Tigers who first used them widely against civilians and even Jews got in on the game before the muslims as Lehi terrorist group who operated in British mandate of Palestine.
Harris was an early supporter of Bush's War on Terror, a supporter of strong decisive action rallying against Western relativism as our greatest weakness. For me, being able to appreciate the context and complexity underlying a view and a variety of its manifestations is a deep strength not a weakness. For me, the War on Terror has exacerbated the problem it has tried to address with the 3rd world (not just Muslim!) perception and opinion of the US at all time low at the end of Bush's presidency, with new and more powerful terrorist groups sprouting in Africa and no progress in the Arab-Israeli conflict.
My sense is that his refusal to look at history, to consider the context and hermeneutics of religion are linked to his criticism of relativism. He is not good at contexts. Contexts are fuzzy, hard to splice, to dissect, to reduce. His is a reductionist materialist approach and for my taste we've had too much of it already.
I know people are impressed by Harris's smarts and his articulate no-punches-pulled defense of his views. But if one digs beneath, I think one finds that his views lack the richness and compassion the world so needs right now. And sadly I don't hold high hope that what he sees as spiritual, being a worshiper of science as the sole arbiter of what is true and what is good, is going to approach the Buddhadhamma any time soon. Working with academics perhaps I have developed a bit of an allergy to the likes of Harris who can actually be decent honest intelligent people, but I just hope that people who have ear of millions can do better.
PS Oh, and their architecture is pretty magnificent! This is a view from the hotel gate where I am staying now: