After viewing this video of Dawkins apparently being "stumped by creationists' question," I did some digging to find his response, giving him the benefit of the doubt that he was likely just trying to frame his answer in a succinct way, or that he was flustered for some reason other than a lack of an answer.
The "creationists' question" is, "Can you give an example of a genetic mutation or an evolutionary process which can be seen to increase the information in the genome?" Dawkins gives a seemingly unrelated answer, so I searched online to find a more detailed written response by Dawkins to this interview, and found it here.
I suspect, from his written piece, that we're mostly talking past each other. He doesn't seem to understand the precise nature of the question (or of information). The question is about how random forces can create new, meaningful information, considering the fact that this has never been known to happen in any area of nature, let alone in biological organisms which must, at all times, be meaningful as a whole in order to survive.
Dawkins does agree to the idea that the information has increased:
I don't think anybody would deny that, by any method of measuring . . . there has been a broad overall trend towards increased information content during the course of human evolution from our remote bacterial ancestors.
But he doesn't address how this could happen or demonstrate how it is currently happening. He merely asserts, "Gene duplications and deletions have occurred from time to time throughout genomes. It is by these, and similar means, that genome sizes can increase in evolution." The closest he comes to describing a situation where this could happen is when he mentions, in passing, an aspect of RNA duplication:
There is a "frame" which moves along the RNA sequence, reading off three letters at a time. Obviously, under normal conditions, if the frame starts reading in the wrong place (as in a so-called frame-shift mutation), it makes total nonsense: the "triplets" that it reads are out of step with the meaningful ones.
So one way new information could come about is through a frame-shift mutation. But, as Dawkins says, these random mutations are "total nonsense." And total nonsense is not "information," since information is meaningful. Is his assertion about "gene duplications," then, confusing the genes themselves with the non-physical information those genes convey? It's one thing to explain the addition of meaningless genes, but quite another to explain the addition of meaningful information.
Here's another excerpt that makes me think he's misunderstanding the nature of information:
Mutation is not an increase in true information content, rather the reverse, for mutation, in the Shannon analogy [see the article for the analogy], contributes to increasing the prior uncertainty. But now we come to natural selection, which reduces the "prior uncertainty" and therefore, in Shannon's sense, contributes information to the gene pool.
From what I can tell, Dawkins is saying here that 1) mutation doesn't add meaningful information, 2) mutation does add noise to the existing simple information content, 3) natural selection reduces the useless noise and redundancy, and 4) this reduction accomplishes the adding of information. The problem, of course, is that natural selection cannot add something that isn't already there--it can only accept or reject what is already present. If mutation doesn't add meaningful information, as he admits, then what does?
I'm interested to watch your comments to see if I've misunderstood Dawkins's argument (as, I admit, is quite possible). I've heard that a certain kind of bacteria demonstrates the addition of information, but I haven't seen the details (I was hoping Dawkins would explain that example), so I haven't been able to evaluate the claim.