This has been a good discussion and I have plenty to say in response. I defined the criterion of dissimilarity as not being consonant with the teaching of the church and used it in the same way as the criterion of embarrassment. That avoided the issues Larry has ably cataloged. I'd hoped to avoid these as side issues, but they are quite valid.
For me, the basic issue is whether, when, and how to go beyond what can be proved beyond reasonable doubt by the criterion to other sayings or actions of Jesus. Of course, I agree with John that a great many things can be asserted as matters of faith that cannot be proved or disproved historically. Still, one cannot just assert that the moon is made out of green cheese when we know very well that it is not, merely because it is more friendly to some religious doctrine we hold. That is bad faith. In that category, I would put the fundamentalists' basically absurd claim that Genesis rather than evolution is science. To say that Genesis has truths to teach us that are not contained in science is one thing; to say that Genesis is better science is absurd.
In the more subtle category of "claimed as historical but unprovable," I would put the resurrection of Jesus. This is characteristic of scholars like N.T. Wright. Trying to verify the resurrection historically is not only impossible but a category mistake of the type that John discusses. Put another way, the resurrection is a matter of faith that should not be replaced by surety, because then it would not be faith. It is significant that Christians disagreed over the nature of resurrection from the first. Some early Christians asserted that everyone had already been resurrected; others denied resurrection completely; still others affirmed that it was a resurrection of the spirit rather than of the flesh. Paul seems to me to speak rather ambiguously about resurrection, suggesting that flesh and blood cannot enter the kingdom of God. That does not make him a gnostic. But it does differentiate him from the rather confident statements of Jesus' bodily resurrection that we find in the Gospels.
With regard to the virgin birth, I would say that it does not pass the test of either the criterion of dissimilarity or embarrassment, and therefore should not be asserted as true by historians. The doctrine of the virgin birth seems to have arisen out of the response of some Christians to the question "How was Jesus born?" We can guess that the doctrine originated largely among Gentiles known to Luke and not among the Jews known to Matthew; in any event, it was not a universal Christian response to Jesus' birth. The fact that the doctrine has a "proof text"—in a tendentious reading of the prophecy in Isaiah 7 of the conception of a "young girl"—doesn't take us to factual. We may find fascinating that Isaiah's Hebrew word alma (young girl) was translated by the Septuagint as parthenos (which can mean either "young girl" or "virgin"). And we may see this as important for understanding how the doctrine of the virgin birth may have taken root—perhaps the idea followed naturally from hearing the Christmas story proclaimed in Greek. But were I a Christian, I would stand with Paul, Mark, and John on the virgin birth. They do not mention it. Neither would I.
There are, however, a great number of teachings and actions of Jesus that are probably historical but do not pass the test of the criterion of embarrassment or dissimilarity. Two that I think have every possibility of being true, or at least having historical kernels: The parable of the kingdom and the parable of Jesus at the money-changers' tables. There are also some wonderful Christian stories, which I love and appreciate, that I think cannot be historically true—like the woman taken in adultery in John. The latter I doubt because the textual tradition of that story is late and poor. But if you asked me about its moral, I would have to say it says as much about the spiritual values of Christianity as any other story in the New Testament.