Well, let me give you a specific example (just one of many): his dismissal of Thomas Aquinas' proofs for God's existence (at the start of chapter 3), isn't even good for an undergraduate; if he submitted that as an essay in a philosophy 101 course, I doubt he'd get good marks. He doesn't bother to understand what Aquinas meant by the terms he uses in his arguments; he shows zero awareness of the historical context, that Aquinas is relying on a specific set of philosophical theories (scholastic Aristotelianism), and it is impossible to properly understand his arguments without first understanding that theoretical background. It appears Dawkins has never read any of the secondary literature (not even a first year textbook!), he is just dismissing these arguments based on a plain English reading of their words. He identifies Aquinas' fifth proof with Paley's argument from design, completely ignoring the (rather standard) position that they are rather different arguments based on quite different assumptions (an Aristotelian theory of causation versus a mechanistic/Cartesian/Humean one)
Personally, I'm sceptical than any of Aquinas' arguments actually work. Maybe, if you accept his philosophical assumptions (about the nature of causation, etc), they succeed – but that leaves us with the equally difficult task of proving those assumptions. So, I think Dawkins may well be right in his conclusion, that Aquinas' arguments fail – but the reasoning he uses to reach that conclusion shows he has zero idea what he is talking about.
To make an analogy – imagine an anti-creationist book written by someone with a very poor knowledge of the science of evolution, and their understanding of it is riddled with errors and misunderstandings, and Dawkins was asked to review it – while he'd of course agree with the book's conclusion, he'd find its contents an embarrassment – much of The God Delusion is the same thing.
Compare Dawkins to someone like the Australian philosopher of religion Graham Oppy. Oppy is, like Dawkins, an atheist. Unlike Dawkins, when he criticises theists' arguments, he actually knows what he is talking about, and doesn't make the kind of juvenile mistakes that Dawkins makes. Unlike Dawkins, he's read all the secondary literature on the topic, and has made significant contributions to that literature. Due to this, many theist philosophers of religion actually have a lot of respect for Oppy, even though they (of course) disagree with his conclusions–among philosophers of religion (whether theist or atheist), Dawkins is mostly viewed as an example of what happens when an expert in one field decides to write a book in a completely unrelated one, and their valuable contributions to the former field are no guarantee their attempt to contribute to the later will be of any value at all.