There was lots of cool stuff in this episode and I have many random thoughts.
Claire is the new Rousseau. Both had babies on the island that got taken. Kate took Aaron because Claire had disappeared and I'm now wondering if there was some similar set of circumstances that caused Ben to end up raising Alex. It's interesting that Claire seems to have gone crazy even though she was the only one of the Losties who was ever inoculated. Oh and it's interesting that not!Locke has apparently been Claire's friend for a while
Hurley's comment about the Adam and Eve bones maybe being one of them from an alternate timeline was something I'd wondered about for a long time. I think there was a lot of speculation way back in season 1 that it was Jack and Kate.
Jacob must not be in Sayid since Jacob is now appearing (like dead people tend to) to Hurley. So then who/what is in Sayid? Or maybe Sayid is just Sayid and the temple people are nuts. I wonder if the bad person Jacob said was heading to the temple was not!Locke... or Claire?
New number! We've seen 4, 8, 15, 16, 23, 42. But now the number 51 is in the mix, corresponding to Kate. The hieroglyphics on the upper wall of the lighthouse (seen behind Jack) were the same as the heiroglyphics that appeared when the numbers would flip in the Swan hatch after pressing the button. The places Jack saw in the lighthouse mirror seemed to be places where Jacob had visited/touched people: the building where Sun and Jin had their wedding, the church where young Sawyer wrote the letter after the funeral. But then there was Jack's childhood house, which doesn't fit (didn't Jacob touch Jack at the hospital at a vending machine?). So what's up with that?
And what's up with alternate universe Jack not remembering having his appendix out? I'm suspicious of the non-reveal of Jack's ex-wife. I would expect it to be the same woman who was his ex-wife in the original back-story, but the fact that they haven't showed her leads me to believe it's going to be someone else (I'm thinking maybe Juliet?). Oh and the fact that Jack's life turned out so very different means the island vanishing in 1977 had a significant impact on his life. I would assume that's because Christian Shepherd's life would've turned out much different, which would've affected Jack's life.
I thought it was odd that Kate was going to look for Claire, but Jack (who knows Claire is his half-sister now) didn't really seem to care. It dawned on me that he really should've been wanting to find Claire ever since he got back to the island.
That's all I can think of at the moment.