AbsurdlyHighDamage Cap: Trailers show multi-hit attacks easily breaking ten-digit damage. At one point, a finishing move is shown to cause a grand total of over six-and-a-half billion HP damage! Even for a Nippon Ichi-associated RPG, I think that's a new record!
One of the screenshots on the website shows an attack doing over 933billion damage.
Amnesiac God: Chou Chou has no idea who she is other than knowing that she's a god.
Bittersweet Ending: The Normal Ending. Chou-Chou abandons her peons in order to destroy Vorgis for good. While a post-credits scene shows they eventually found her somewhere at the edge of the universe, and can speak with her, she is unable to come back with them. Thankfully, it seems this ending isn't canon.
Calling Your Attacks: A variation with Soul. When casting a spell, he'll say "Spell" and then just say whatever it does. Such as "Spell! That magically teleports me safely to the castle!" Or "Spell! That heals all wounds in a flash of light!".
Censor Steam: Necessary for the various bath scenes, and in the Japanese version, a small extra mechanic to the hot spring minigame.
You can customize the clothing of everyone in the playable party, including the main characters.
Cloning Blues: A few of your party members get cloned for some bizarre reason in the post-game and you must fight them with their levels in the 1000 range. Good luck with that by the way, unless you've been Level Grinding at the Mugen Field.
Disc One Nuke: it's pretty easy to wander into the Mugen Field at early levels, get into a random ship battle and get a huge EXP bonus, propelling your party forward 20 levels or more, pretty much steamrolling the rest of the main story for a time.
Generally that could be bad, but in a game where you can increase the level way higher than you should, it's a pretty good thing.
Duel Boss: Chou-Chou has a one-on-one match with Belleria.
Elemental Rock-Paper-Scissors: Personalities in Mugen Souls act as elements, and have corresponding strengths and weaknesses. Incompatible personalities will reduce the power of team attacks, adding a certain degree of strategy to party formation.
Pragmatic Adaptation: Nippon Ichi has announced some changes will occur to the US version of the game, presumably this will involve removing or editing the extremely lewd bathing minigame. And possibly the post-game post-fight CG of clones of your allies.
Confirmed. NISA has stated the bathing mini-game will be removed in it's entirety.
For more info on this (and link about it), see Bowdlerize above.