Is he an ex-husband, boyfriend? If he was a boyfriend, how involved were they? If it was casual dating a few times, that's one thing, but someone she was involved with more than that, well, I know I wouldn't like it.
Another thing is, when you friend someone on Facebook, they pretty much are gonna know your whole business if you post about everything. I don't know how involved with Facebook your wife is, but if she posts personal matters, that's another thing I wouldn't like.
Do you have a Facebook page as well?