Select all, go to the groups tab and hit the "Auto smooth" window, then go to the Wetex tab and press "Unweld". Then go back and hit "Auto smooth again and then go to Wertex->"Weld together"
EDIT:
Select the black faces, go to 'faces' on the top menu and hit "reverse vertex order"
I think that is not the problem, but then you must be in the flat shaded wiew and then do the ^ procedure.