I'm redating this post, because I noticed that Vinny has a post on his blog which essentially uses the WCA against my position.
Dr. Logic's argument is what I have called the Inadequacy Objection, or we might also call it the Wild Card Argument. The idea is that theistic explanations don't really explain because they don't give you a reason to supposed that event X was expected as opposed to event Y. God had the power equally well to bring about X or Y, therefore, to say that he caused X doesn't really tell us why X was caused and not Y. Playing the God card is what you can do anytime, anywhere, and so it really doesn't do any real work.
We might believe that X is more in character for God than Y, and therefore X was more to be expected than Y given the existence of God. But here, I think, a kind of empiricism about the sources of our probability judgments is employed. We actually haven't seen God perform this act or that, and therefore we have no basis for believing that God is more likely to do this as opposed to that.
I'm not a pure empiricist about the basis for our probability judgments, and in fact I think that frequentism in probability theory leads to contradictions. But the Wild Card Argument is far from silly. Defenders of theistic explanations had better learn how to counter it.
My Infidels paper on Hume on miracles covers this issue, and I like to it here.