Found a good, clear article here which picks up four problems with memes.
Briefly these are:
1) the definitions of replicators/phenotypes are confusing or ambiguous
2) the evolutionary model associated with memes is Lamarckian (3 legged dogs have 3 legged puppies) not Darwinian
3) memes often used instead of genes (i.e. memes are often called in to play as explanations for cultural preferences when simpler/more rigorous sociobiological explanations can be used)
4) the notion of self – the idea that, while being at the mercy of genes and memes, we can pick and chose the memes that help us.
Meme problems: http://jom-emit.cfpm.org/1998/vol2/rose_n.html