Specifically, how does the revelation that his wife is a spy harm Joe Wilson’s credibility or character?
The issue is that it destroyed his wife’s career.
The implication is that he was biased based on his wife’s profession. That he would make decisions based on personal bias goes against his credibility.
Haj
As I recall, the current hypothesis is that the intent wasn’t to cast doubt on his credibility or character, it was to make an example of him by showing other diplomats/politicians/foreign service employees who publicly disagreed with or spoke out against the administration what could happen to them or their families. If you’re serving in a foreign country that has, at best, tense relations with your home country, the last thing you want is for you or one of your family to be revealed as an intelligence agency employee.
Not only that, but Wilson’s career as a diplomat is probably severly curtailed if not outright destroyed–he can’t be posted to possibly hostile countries anymore, because his wife (and he) could be at risk. And it’s probable that his “opposite number” wouldn’t deal with him as openly since the suspicion would always exist that Wilson is passing information onto his wife. No doubt there are even more repercussions that I’m not thinking of right now.
Mind you, it’s only a hypothesis that the Bush administration leaked his wife’s status to the public, and that it was done in retribution for Wilson’s public disagreement with the “Iraq is trying to get nuclear materials from Africa” assertion. As far as I can recall, the matter is still “under investigation”, with the Bush White House denying that they had anything to do with it.