There's not much, but a few things are, I feel, helpful innovations that add to the series.
- The addition of the training mode.
- Changing weapons mid-combo allows you to continue your combo with the swapped weapon, instead of resetting it as in previous games.
- If you save and quit mid-mission, then load, you start right where you left off.
- Boss fight have now their own separate missions, sans the Hunter fight.
All of the above are adapted from Bayonetta in some way, and are features that should be in later installments. The training mode can be improved by adding fighting game-type statistics showing e.g. how much damage a move does. Also a tutorial mode where players can learn the finer points of the combat system, such as functions of enemy step, weapon/style switching and cancelling, invincibility frames and so on.
I feel Dante's movement controls were improved as well, though it certainly is different than past entries and requires getting used to. Dante's running speed is faster, and his jumping has more maneuverability as it can be controlled mid-air.
The movement controls are almost as good as Bayonetta's, but could be better than even there, like the jumping needs more forward movement and more control. I'd like the return of sprinting from DMC4 as well, but it should be manual like Bayonetta's beast run.
At the same time, there are a couple of improvements to earlier series features, like the upgrade system, which is one of the user friendly streamlined features that works better. And the Angel and Demon modifiers allow the player to choose any of Dante's melee weapons without having to shuffle through them, like in DMC4. Obviously you still have to shuffle between firearms, which could have been avoided if they took advantage of the down button on the d-pad.