I am reading Dawkin's book with the above title. A couple of thoughts occurred to me as I read the chapter entitled "Why there is almost certainly no God."
1. If Darwin was correct in highlighting the discovery of a complex organ which cannot be produced by numerous slight successive modifications as a real possible falsification of his theory then we cannot simply rule out any such proposed organ as a "God of the gaps" argument. If the God of he gaps protest is permitted then the possible falsification has gone. If the falsification is a genuine possible one then we must allow for the existence of real gaps.
2. Dawkins argues that an intelligent designer must be more complex than the evidence of his design and therefore requires a further explanation of an even higher level of complexity. He seems to indicate that this is a sort or killer punch as if the rule of the universe is that all complexity must necessarily come from simplicity. However the fact that he spends time on other arguments seems to indicate that he is not entirely happy that his killer blow has actually killed.