Save the game when prompted after the credits. That saved game file will be marked with a star when used to start a new game and will have the following bonuses. The customize menu will have options to view all cutscenes, all dialogue, and all camp/help skits. There will be a bonus dungeon called "Nereid's Labyrinth" at to the Orbus Barrier.
New Game + Rewards
After you beat the last boss and the credits roll, you will be asked to save. Create a new save file, and when you start it, you will start a new game, but your save file will haev a star next to it, and you will have access to even more stuff.
Effect - Task
Nereid's Labyrinth Dungeon - In a New Game + file, go to the Orbus Barrier to find a new dungeon
All dialogue - Go into the Customize menu of a new game + file
All cutscenes - Go into the Customize menu of a new game + file
All camp/help skits - Go into the Customize menu of a new game + file