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Man, this is gonna be a long list. Anything you notice that's been recycled, be it themes, names, or whatever, list 'em! I'll just put a few things I can think of off the top of my head for now.

1. Summons: Besides the actual summons Odin, Alexander, Shiva, and Bahamut, you also have a lot of the fal'Cie. There's Carbuncle, Eden, Anima, Kujata, et cetera...
2. Cid: Raines! God, I love him.
3. Mascots: I've seen chocobos, moogles, cactuars... at least referenced, if not technically appearing.
4. Monsters: Flans, behemoths, adamantoises, sahigans, and so many others.
5. Airships: Obviously.
6. Trains: They played a big part in VI, VII, VIII, and they show up a surprising number of places here, too.
7. Names: Palumpolum from the twins' names in IV, Lindblum from the city in IX, Palamecia from II...
8. Weapons: Again, a lot of them, including Ultima and Omega Weapons.

I'll name more later, too.

That was Carbuncle! whee And yeah, I'm pretty sure that was Ifrit, but I wasn't entirely sure of any of the others.

One more thing I didn't mention before: Crystals, of course! That would be in the Crystarium, and people turning to crystal, and I suppose the Eidoliths.

I was going to say that the lady with the harp looked like Siren (or is the Siren?), but I wasn't a hundred percent sure since I've only seen it in VIII (and that was a long time ago).

I have another reference though, but I'm not quite so sure about it. I remenber watching Advent Children a while ago and I believe the first scene depicted the land and had some of the Red XIII creatures running across it (sorry for my poor description, but I haven't played VII so I don't know many specifics). Then during the opening sequence and scene that played when you first emerge in Gran Pulse, it showed a bunch of the wolf fiends of XIII running across the plain in much the same way. I'm not sure if that's a reference, but it just stood out to me in a nostalgic kind of way.

Edit:
I actually just found one more when I was perusing one of my favorite websites that lists different cross-overs from the game. It seems that Serah shares a name with the Princesses Sara/Sarah from I and III respectively. It is also the secret name of a certain character from IX. Just thought that was interesting, specially if you're into names and name origins.