Important: The way to fix the problem is right click on the Divinity 2 icon and go to propertaies. Go to the compatibility tab and select "disable desktop composition" and if you are on Vista or Windows 7 select "run as administrator" and apply. The game works correctly after that.
I have tried the obvious already and it doesn't change anything.
This is not a problem with the OS, probably something with graphics settings. I'm going to check with the engine guys tomorrow.
So...