Thanks for this; it's a useful article. I think the authors's view of the role of intuitions is probably too simplistic. This assertion in particular gets things really and deeply wrong as a description of philosophical practice:
"In many traditional and contemporary philosophical projects, when an intuition is invoked it is assumed that the propositional content of the intuition is likely to be true, and thus that the proposition can be used as evidence."
Especially, I don't think that intuitions matter because we think that they are true, but simply because, when properly interpreted, they are what we think, true or not. If we're in the project of theorizing over what we think, then that we think something at all, true or not, has to be part of the data we are meant to theorize, and is significant simply for that reason. (Sosa is wrong that intutions are like observation; they are not; they are like data.) So maybe it is true to say that intuitions count as evidence for and against philosophical theories, but, if so, it is only in the way that data generally counts as evidence for or against a theory which aims to theorize over that very data. [Ed.- Anyway, what matters is that the role of intuitions as thought, and the role of thought as data, as objects of theorizing, as stuff which philosophical theorizing is chiefly about, should not be obscured.]
The example of Gettier cases shows what I'm getting at nicely, I think. It doesn't matter if you fail to have the relevant intuition in 100 such cases-- so long as you have it in one, you have a contradiction within your thought (if you are committed to the JTB theory of knowledge, that is) which you need somehow to resolve. Even one such Gettier intuition creates serious trouble for the theory, no matter how often it is that JTB seems to work as an account of knowledge. (And of course JTB *does* seem to work in lots and lots of cases, or else it wouldn't have ever been a serious contending theory in the first place.) But that just means that intuitions aren't like weights in a balance which measures evidence v. counter-evidence and so gives us the measure of a theory's truth.