@ZipLine-- That's a really good question and a difficult one. But I think this part of the Clause would decide your question: "And the Congress may by general laws prescribe the manner in which such acts, records, and proceedings shall be proved, and the effect thereof."
So at the end of the day, Congress will decide whether and how other states recognize each other's laws and decisions. If Congress were to rule that all states have to recognize same-sex marriage (which is complicated in an of itself), I guess they would have to.
But this is not just an issue about the faith and full credit clause. It's also about the definition of marriage, which I think is up to individual states, so it's a really complicated case.