They could have had their "marriage" blessed afterward. I believe their is a 1-year waiting period.
Kerry himself has never been able to provide evidence of an annulment. All he has said is that he "applied" for one, although he doesn't say when he did this (probably just before the start of the campaign!).
He was married in a civil ceremony on his lawn (or maybe it was the lawn of his lovely wife...). If he later got an annulment he could then have regularized his situation, but it doesn't sound as though he ever did. I suppose it's also quite possible that the annulment was refused, because I believe his first wife was undergoing a nervous breakdown at the time.
In any case, he's never made it clear. The thing that has probably prevented this from coming out is the fact that he attends the left-wing "Paulist Center" in Boston, which like him is Catholic in name only.
Depends on how much you give to the church.