What makes this one in particular "really bad" is that if "Mary was a lying adulterer" was the most likely explanation for the story of the virgin birth, this could be justified on the grounds of pointing out an uncomfortable truth. But, given the timeline of accounts, the actual most likely explanation is that the whole virgin birth story was made up several decades after the supposed date of the Crucifixion as a soldier argument for "Jesus was special", and nobody on the "Jesus was special" side was willing to attack it.

So, instead of a powerful example of how "arguments are soldiers" turned a ridiculous idea into a dogma of both Christianity and Islam, we got a minor rewrite of the story of the Toledot Yeshu, with a rabbi replacing a Roman soldier as the lying Mary's adulterous lover. Because the original Toledot Yeshu was apparently such a breakthrough in rationality-promotion.

More or less my thoughts.