What is causing speckling of these stems?
I think you are looking at low vigor and several other problems. The tan coloration of the bark on two year old shoots is the death of the external cells of the new back forming a protective layer on the stem. This is normal and often occurs on the portion of the stem most exposed to the sun. The speckling may be due to disease or some other stress. The speckling looks bad, but is not really a symptom of any specific disease.
The black coloration on last year's shoots is called sooty blotch in Michigan. It is caused by a group of fungi growing on the waxy cuticle of the stems.
In New Jersey the condition is called black shadow and some growers believe it does cause problems when it is severe.
I see a lot of lichens growing on the older stems which indicate to me that fungicides are not being used. Are you an organic grower? Lime sulfur would be an effective preseason dormant spray which is organically approved. Sulforix is a common commercial lime sulfur material but I am not sure if it is OMRI approved.
Before you go spray the bushes with lime sulfur you should also know that you have Lecanium scale. Those are the dark brown spots on the 3 year old stem to the left in the photo. The easiest control is a dormant oil spray and oil and sulfur are generally not compatible and should not be applied together, nor should the applications be close in time when there is green tissue available as the oil will carry the sulfur into the plant causing phytotoxicity.
The bushes in the background do not look like they have been pruned in a while. I would suggest you remove 2 or 3 of the oldest canes to get new growth in the bushes. Several of the oldest canes should be removed every year to maintain new growth from the crown.
Mark answered this question well. I also wanted to add that if this is cultivar Elliott, it usually has what we call "ugly bark" or "measles" with a lot of scabby and irregular flecking of the stems. That seems to be characteristic of the cultivar and not related to any particular disease although it may be worse in stressed plants.