Question
On one of my viburnum shrubs (snowball)the leaves have white/grayish spots on the upper surface and eventually the leaves turn black, curl and fall off.  There are also some of the same white spots on the branches as well.  New growth looks good for a while, but then does the same thing.

Answer
I would check for scale insects first.  These will be oval in shape and may be covered by a white cottony substance upon first inspection.  These insects do not move and can be scraped off with your fingernail.  Let me know what you find.  The other possibility is powdery mildew, but it doesnt affect the stems.  Respond back with your findings and I can recommend a control.  Thanks.