A Moorean fact, roughly, is any proposition of which I am more certain than the premises of any argument to the contrary (I ignore for simplicty the implicit category error). So construed, I suppose I don't believe that there are any Moorean facts; there just are no individual propositions (or at least very, very few) that I am willing to hold onto "come what may".
Nevertheless, it does seem to me that there is a generalization of Moore's idea which is somewhat more compelling. Define a possible situation as a consistent set of propositions (with a possible world being the limit case of a maximally consistent set of propositions). Then, a Moorean situation is a situation which I am more certain obtains than the premises of any argument to the contrary. [Of course, every Moorean situation is equivalent to some Moorean fact, but put that aside. I refrain from defining a Moorean situation as any situation consisting entirely of Moorean facts.] For what are I suppose obvious epistemic reasons, I don't believe in Moorean situations either.
However, I do find myself inclined to accept "quasi-Moorean situations". A situation S is quasi-Moorean iff I am more certain that "a good many" of the propositions in S are true than the premises of any argument to the contrary. In particular, I think that situations composed largely or entirely of propositions which have a reasonable (if mistaken) claim to being Moorean facts will end up being quasi-Moorean situations.
Now I doubt that quasi-Moorean facts will do very much epistemological work for us, so I don't think that this generalization of Moore's idea will have much bearing on Moore's concerns. However, it might do some interesting metaphysical work for us ... about which more next time.