it comes in pints?

No, it doesn't. I'm not sure of the exact reasoning, but a marriage is presumed valid unless it's called into question, and so children conceived in a presumed-valid marriage are legitimate. So nullity of marriage is retroactive (i.e., the marriage was invalid from the get-go), but legitimacy isn't. This DOES render Joe's second marriage invalid, though.

I'll have to ask Christina about it; she knows canon law a lot better than I do.

Yeah, I actually assumed that illegitimacy requires knowing it's not valid at the time. Although I really hold to Dear Abby Landers's take on the whole subject - there are no illegitimate children, only illegitimate parents.

But what's really funny is that as I clicked to see your comment, I was taking a sip from my beer mug and at first read that second part as "I'll have to ask a Christian about it..."

Sorry, man.

No, the children are considered legitimate.
Most annulments are about something wrong with the marriage from the beginning: in the case of the Kennedy's it is because the men never thought the vow to be faithful to their wives meant anything. Other reasons nowadays are immaturity (you got married at 17) or family pressure (you were pregnant).

Other reasons might be that you are close cousins (many of the royal annulments in history are for this reason...alas for Henry VIII, his first wife didn't consummate her first marriage, so and she appealed and won). And if a husband is gay and can't have sex, you can get an annulment.

Kennedy's wife is the wife from hell. She isn't even Catholic, so the annulment means nothing. It's just her way to revenge herself. However, he probably lied to the tribunal to get away from her, so she has a legal point.