Jeremy Burman recently reminded me of one of the bits in The God Delusion where I think I disagree with Dawkins. On page 223 Dawkins says:
The central question for meme theory is whether there are units of cultural imitation which behave as true replicators, like genes. I am not saying that memes necessarily are close analogues of genes, only that the more like genes they are, the better will meme theory work; and the purpose of this section is to ask whether meme theory might work for the special case of religion.I prefer the strategy of much of mainstream cultural evolution to what this sounds like. There's not much point in having a science that only deals with some kinds of cultural inheritance - because most of the math (e.g. of frequency analysis) is pretty-much the same for all kinds of heritable cultural information, so you might just as well have a science that covers the whole subject - which I think can still reasonably be called "memetics".
The best domain to study has proved to be a tricky problem. Boyd and Richerson (1985) proposed the domain of study just cover information transmitted via imitation and teaching. Blackmore (1999) propsed the domain just cover imitation. None of these seem to me to "carve nature at the joints" very well. I think the most obvious domains to study are: social learning and all learning. Social learning is what most people have looked at so far - e.g. see Mesoudi's 2011 book. However, all learned information evolves together in the brain. Of course, covering all learned information would be a radical expansion beyond most previous evolutionary thinking on the topic.
Dawkins seems to be thinking about having a science of memes that only covers a subset of social learning. That is almost certainly not the way to go, IMO.