One of my favorite aspects of Epic Mickey was the use of the old cartoons as gameplay. I learned through the game that the old Mickey cartoons were so animated, and that made for awesome platform jumping. It was neat to have theme-based transitions between worlds, but I think the formula should be changed.
The other aspect of Epic Mickey was the exploring of the lands. These are always fun. In particular, there should be more puzzles, more happenings - like the rising of the nautilus. Thinning paint should not only open holes, but cause more changes in the world - like columns falling and breaking new things and making new bridges. In fact, the order in which one thins and fills should affect the environment.
My ideal for Epic Mickey II is a remix. The outside 3D world should me more continuous - no transition levels. The cartoons should now be more elaborate and unlock powers to help you in the main world. For instance, the jungle level should unlock little coconut throwing monkeys, the haunted house unlocks ghosts - they help Mickey.
I would make the game more advanced for the better players, but include things to help less experienced players. I would do this by having lots of puzzles that are available, but not necessary. I would also have hints that you can purchase, as an example. Maybe you could use the magic mirror to reveal hints. Also, for battling enemies, I would make the enemies tougher and have more staged battles. This way, specific techniques can be used to attack the enemies (like using the ghosts to scare them so they are vulnerable). The large number of techniques will make the game exciting for experienced players, but the hint system will make it very easy to beat once you know the right technique.
One thing I didn't like about Epic Mickey was that it was full of rich worlds, and yet they felt rather empty. Maybe now that Wasteland has been saved, it can be more alive. More characters walking around and doing things.
IN FACT - perhaps the new enemy is sneaky and sinister, so you wouldn't find a wasteland plagued by open disaster. Instead, you find a world alive and robust, but with hints of bad things going on, rumors.
Or, you could have "Oswald's Waste World". Now you have Epcot basically, as someone mentioned. The 'monorail' system that connects them could appear to be obscenely high-tech, just for fun.