The first time I read this chapter, I liked it, but I also mentally totted up all the various theistic manoeuvres that might be made in response that Dawkins didn't cover (how could he, in a single book?)
On a second reading, I am rather more impressed. Dawkins does actually cover a remarkable number of possible rejoinders, and he does deal with them pretty effectively (though the knock-about style will convince some that Dawkins is not being rigorous, close reading reveals that Dawkins's treatment of objections is pretty well thought through).
The central idea is, of course, that while theists appeal to a cosmic person or intelligence to account for features of the world that, they insist, are otherwise inexplicable, such as "irreducible complexity" - the bacterial flagellum, say, or the seemingly fine-tuned character of the universe as a whole - the appeal to God is, inevitably, an appeal to something that is itself highly complex. A God capable of designing a universe would have to be an immensely complicated being - his mind would have to be far more complex than our own, for example.
We have a here a regress-or-turtle- type objection of course. If complexity requires a designer, then God's complexity will require a designer, and so on to infinity. Or the theist can say "God (like the ancient Hindu's turtle, which was deemed the exception to the rule that unsupported things fall) is the exception to the rule that complexity requires a designer". But why play the exception to the rule card here, rather than at the right at the beginning, with the first complexity to be explained?
Note, by the way, that Dawkins is not just finding fault with this kind of teleological argument for the existence of God. After all, to fault an argument for x is not to show that x is not, or is probably not, true.
Dawkins is also making the point that God's complexity itself makes him a very unlikely, improbable being.
A possible theistic response
I suspect the point at which most theists will want to attack is the claim that God must be complex. Swinburne suggests that the values zero and infinity are the simplest values. If you are giving, say, a subatomic particle a property of value n, and deciding what n should be, infinity is a simpler suggestion than, say, some very, very large value.
If that's correct, then perhaps, by suggesting that God's mind and intelligence is infinite, the theist can maintain that God's mind is actually simpler than, say, our own. So appealing to God's mind to account for, say, the complexity of our own is to to explain a more complex thing by reference to a less complex thing. In which case, Dawkins's objection fails here. More generally, if God is of infinite intelligence, wisdom and power, that makes him a really rather simple thing. In which case, appealing to him to explain complexity in the world does not raise the problem Dawkins thinks it does.
Is this a good response to Dawkins, though?