Fan Nickname: The Warriors of Cosmos and Chaos are sometimes simply called Team Cosmos and Team Chaos.
Some fans call Onion Knight Luneth, for the first main character of the Final Fantasy III remake. Onion Knight's alternate outfit even makes him look like Luneth. Fans who don't try to insist he's Luneth generally call him OK or Onion. And since his hair and armor looks like Onion Knight Ingus, some fans call him that instead of Luneth.
I Knew It: Though the rest of the series including the original Dissidia merely hinted or implied it, Dissidia 012 confirms 100% that all Final Fantasy worlds are connected through the Interdimensional Rift and are part of the same multiverse.
In the same way, Gilgamesh, Shinryu and possibly Omega (Weapon) are the same entities whenever they appear, just taking on different forms as they travel between worlds.
No Export for You: Dissidia Final Fantasy - Universal Tuning, yet another example of Square's tradition of Japan-only updated re-releases. However, in an interesting situation some people prefer the North American and European release over Universal Tuning, as numerous characters had their ability to cancel certain attacks removed, resulting in the combo potential of some characters being shattered.
As of Dissidia 012, the Official Quests, which is disappointing because as short as they may be there's a lot of plot holes they fill, such as how and why Sephiroth killed himself in the 12th cycle, the travels of the original cast during the 12th cycle, and the continuing exploits of Gilgamesh, Shantotto and Gabranth. This is possibily due to an oversight with the Quest mode though; each text screen is limited to 25 characters, not a problem for the Japanese due to their writing systems, but a big problem for English speakers. Thus converting a quest to English with all the dialogue intact could simply be impossible. On the other hand though, thanks to the Quest system there's nothing from stopping fans from trying it and releasing them for download.
Vaan is voiced by Kensho Ono rather than Kohei Takeda. Square-Enix said they couldn't finalize a deal with Takeda but didn't want to cut Vaan, but some fans suspect that Takeda was dropped because he "spoiled" the surprise by reporting on his website that he was going to be in a new Final Fantasy game.
Urban Legend of Zelda: In the grand Final Fantasy tradition, it's accumulated a few, including claims of Chaos being playable without hacking the game (and his summon Shinryu being usable by the player). It was also (briefly) the subject of a widely believed hoax by a French gaming magazine, which created fake screenshots of Lightning, from Final Fantasy XIII, as a playable character in the Universal Tuning version.
What Could Have Been: Initial trailers of the game showed plot-elements that never appeared in the game, such as a scene with the Emperor, Garland, Kuja and Ultimecia telling Squall and Firion about Cosmos' true nature being the one of a Goddess of Death, suggesting that Light Is Not Good. Also, the dialog before the fight between Squall and Warrior of Light at Memoria is about the purpose of the crystals, and the latter knowing something Squall doesn't, but that doesn't seem to be nice to know. In the actual game, though, all these elements aren't shown at all.
In another example, trailers showed Garland irritating Kuja and the two of them fighting. In the finished product, all that happens in a cutscene, and it doesn't go any further then them preparing to fight until Jecht shows up, at which point Kuja takes off.
There was also some backstage talks about the consideration of Lightning making it to the roster, but was shot down because Dissidia was released before XIII and Lightning's inclusion would spoil the skills that she'd use in the game. There's also the fact that they considered Seymour, but opted with Jecht instead since Seymour has more emotional links with Yuna instead of Tidus. Or also how Nomura seems to really wish Kain Highwind to be in as Cecil's rival, but thought otherwise in the last seconds and put Golbez instead.
And now with the prequel, the developers considered Eald'narche or Kam'lanaut to represent Final Fantasy XI on the Chaos side, but decided to go with Prishe, who was originally considered for the first game but was left out in favor of Shantotto.
The "Goddess of Death" point was eventually resolved in an Official Quest, where Cosmos comments that she's a Goddess of Death due to her existence keeping the cycles going while her warriors keep getting killed off each time.