Pinging Odder, maybe you can better articulate what Harris' fundamentally flawed ideas are? I'll take a stab at it but I don't know enough about the topics he discusses to be certain of my position. (I apologize in advance for the snarky tone.)
There's two things which I noticed while reading that piece. One is his eagerness to point to Islam school of thought as the main reason for atrocities. We burned witches because of our medieval believes, so now that Those Scary People burn people with acid it must be because of their medieval belief system. Let's blame that instead of the complicated geopolitical situation, the completely media-aware terrorists hitting weak spots, the economic interests in the area, [insert actual reasons here].
Secondly, as a Man of Science, he thinks that (religious) beliefs are the root of all evil and that it must thus must also be the solution. Thus, he seems to assume that if we change the minds of these morally and politically deprived people, everything will be alright and violence and tribalism will be a thing of the past. Islam, save the world! Of course, he combines it with a healthy dose of superiority, so our set of beliefs are never a problem since they are Enlightened and Secular and Based on Science.
I mean, how else can you write something like this without irony:
We live in a world in which people reliably get murdered over cartoons, and blog posts, and beauty pageants—even the mere naming of a teddy bear. [...] We want secular, enlightened, liberal Muslims in America.