I mean, the big thing other than the Islamophobia is that Harris seems to think that science can solve philosophical problems, but if he took the time to really understand those problems, he'd realize they don't and can't have scientific solutions. For example: He thinks that science can determine ethics by empirically determining which moral systems produce the best outcomes, or that science can prove whether or not free will exists. But, what he doesn't realize is that it's the role of philosophy to determine what the best outcomes even are, and that his scientific disproof of free will contains a philosophical presupposition that free will doesn't exist. He wraps his bad philosophical ideas up with the power of modern science, hoping that will strengthen them, and it usually works because a lot of people really trust science and don't really know or trust philosophy, so his ideas get a lot more traction than they deserve.
I could probably go bit-by-bit into why each of his ideas are so flawed, but honestly it isn't worth the time, for the same reason it isn't worth debunking the arguments of creationists or flat earthers. It isn't really about whether or not free will exists the same as it isn't really about all the geological proof for an old, round earth. It's about what we use to evaluate whether the beliefs we have are true or not, and just like religion can't solve scientific problems, science can't solve philosophical problems. Although the creationists sometimes appear to be using scientific arguments, and Harris appears to be doing philosophy, both arguments are rooted in a completely different epistemological structure. Harris lives in the world of scientific empiricism, and wants to debunk or verify things, much like many religious people live in a world of dogma, and that leads them to methods and questions that don't work so well in other fields.
By the way, the reason Harris gets so much hate in the philosophical community isn't just because of this, but because he's completely uncharitable. He has the mindset of a lot of people in the scientific community, that people just sat around being dumb and believing in a flat earth and Aristotelian physics until the Enlightenment came along, so to him it's plausible that a lot of people now sit around being dumb thinking that free will exists or that ethical problems are difficult. That really comes off in the way he speaks and writes, as if he believes that he's looked past all the troubles that all the smart people who came before him and found the easy solution, rather than consider that maybe the fact that so many smart people have considered these problems before him means that the problems don't have easy solutions.