Question
I live in Northern California and noticed that (one of many different types of trees), the fruitless mulberry was being covered on the branches with this orange 'stuff', it looked like it had been awhile because most of the tree is covered or has it one it.  Now I'm looking at all my trees and bushes and finding it just about on everything,(but little spots here and there, from my dogwood, maple, liquid amber,spirea bushes, oak trees, weeping willows( leaves are yellowing and spotting), fruitless pears, Asian pear and persimmons.  My local nursery sold me a bottle of "Bayer Advanced 3-in-1 insect, Disease, %26 mite control.  It makes up to 12 gallons and it is a spray, I just can't imagine trying to spray some of the huge trees.  I don't think they all have the same problem.

Answer
This sounds like a rust fungi. Mulberry rust is common in China where they raise silkworms on mulberry leaves. It is not really a serious leaf disease as far a causing the tree any health problems. It may cause some of the leaves to drop early. The only control I could find was the use of a fungicide but this would have to be sprayed on all the foliage weekly  in the spring  for about a month. It does not seem very practicable in your case. I would not really be too concerned about this rust disease on the leaves. For a rust to infect a leaf the conditions need to be right--humid and warm spring. I do not think it will cause too much of a problem. And may not show up in future years.  

In severe cases,the spread of the disease can be controlled by timely raking up of fallen leaves and also by spraying 0.2% Kavch (Chlorothalonil) or Folaf ( Captofol) 2 times at an
interval of 10-15 days