This was a nice extended argument in favour of a virtue-theoretic account of knowledge. Greco makes some nice arguments for why other theories of knowledge (namely deontic, internalist, and evidentialist theories) are inadequate, and why his form of virtue-theoretic epistemology avoids problems that are generally posed for theories of knowledge, particularly reliabilist ones.
One concern I have with his account, which I think is nicely discussed by Pritchard in The Nature and Value of Knowledge, is that it seems that an event can be both an achievement and lucky (which is not permissible on Greco's view). On Greco's view, achievements (such as knowledge) are produced through an exercise of skill, and such exercises cannot be lucky, so achievements (such as knowledge) cannot be lucky. But if achievements can be lucky, then we can design cases such that an agent produces some event (e.g. forms some belief) through the use of a skill, but where this is not knowledge due to the presence of luck.
I'm also a bit uncomfortable with his attributor contextualism, as it seems implausible to me that claims of knowledge can differ merely depending on the interests of the attributor (which can include the interests of the subject to whom the attributor is speaking, on Greco's account). On his account, the truth of knowledge attributions can vary according to the practical interests at play in the attributor's context. It is not just that the truth values of knowledge attributions can differ according to how closely we are considering the epistemic warrant (or what have you) for some belief; the practical use to which this assertion of knowledge is being put can alter its truth value. This just doesn't seem right to me, and it is key to making sense of his account (as it partly underpins his account of causal explanation, which underpins whether a belief is produced because of the exercise of a virtue).
These are just my initial thoughts, so I'm not deeply committed to them. Overall, the book was well worth reading. (For those interested, I also found the NDPR review by Richard Fumerton interesting.)