Wow.
I was skeptical as all hell before the demo, watched a lot of gameplay and thought it looked very crude and slow compared to past Devil May Cry's. After playing the demo though this will be a day one purchase for me. Loved everything about the first demo level. It's really hard to say where this could rank amongst other Devil May Cry's, but as a game of it's own it's pretty damn good.
Glad there was a demo, might've completely dismissed this without one.
As for what I liked, the story is really hammy but it's different compared to a lot of recent stuff. Dante is surprisingly likable, his banter/dialog is actually pretty entertaining. Combat was confusing at first due to controls but it's very snappy and responsive.
My main beef with the game so far is the UI. Absolutely dreadful. Looks like a placeholder for a finalized UI.