I don't have time to comment on it right now, but I will say I'm of mixed feelings on it. I disagree with little of the positive claims they make but a lot of the normative claims they make. I'll try to elaborate later.
Market failure is in quotes in the title because the term always bugs me. I've pointed out before that it's kind of a misnomer. A market isn't failing, really. The problem in most applications is that there is no market! It seems silly to say the market fails in that case. The term is pervasive so there's no fighting it really - but I try to use terms like "externality" or "asymmetry", which are more descriptive of what's going on anyway.
David Henderson has thoughts on the post here.