First of all, in effort not to distract from Jay's post (which I think covers more important issues than this one) I'll commented on it soon and encourage others to do the same.
Williamson spends a fair bit of time on a point made by McDowell. He claims that there is no fundamental gap between what is the case, and what is thought to be the case. Throught this thesis, he could be considered a follower of the conceptual turn. He definitely follows the first two thesis of Dummett. Williamson makes a few argument against him (most of which I think are sound), I'll focus on one that may be unsound:
1) What one thinks is individuated at the level of sense
2) What is the case is individuated at the level of reference
4) if (3) then (5)
5) What one thinks is the case distinct from what is the case
I think this argument could be resisted. McDowell states "When one thinks truely, what one thinks is what is the case"(page 8). If the object of thought are propositions, and propositions consist of something being some way (if true), then premise (1) can be denied. Dummett's second thesis can be brought in to say that (1) is really speaking of the psychological process of thinking, NOT thought. Perhaps this is one of the weaker readings Williamson eludes to.
On to the point about elusive objects. If the drive of this discussion is to obtain a methodology for philosophy, I don't see this as relevant per-se. The presence of elusive objects would make McDowell's claim false, but I don't think it would undermine his justification of the conceptual turn. Elusive objects cannot be studied anyway, so from a methodological standpoint they're not too significant. However from a metaphysical standpoint I think Williamson is dead on here.