One possibility is Twig Blight, Seifertia azaleae. Azalea and rhododendron branches can be affected by this disease. The disease is characterized by a grey powdery fungal growth. A mass of gray spores may be produced on leaf and branches surface. Infected shoots bend over at the lesion and may remain crooked or die back. Purple varieties are more susceptible to this disease. True resistance is not available as this is an opportunistic pathogen. To help reduce disease incidence, growers adjust plant spacing to reduce humidity and increase air circulation.

Azaleas that are sheared like a hedge are more prone to this problem. When pruning azaleas, one should open up the plant so that air can flow inside the plant. Use of hedge pruners is not advised because of this problem it causes.

Since you mention that the spots are green, I suspect that it is not Twig Blight, but is lichens. Lichens are curious & highly successful composite organisms consisting of a fungus growing in symbiotic concert with an algae, so that lichens become the only fungal organism capable of photosynthesis thanks to this union. Photosynthesis, hence the green color. However, lichens do not kill anything. They are just along for the ride, so to speak. They just sit there and generate their own nutrients.

Some people do not like lichens. Others prize them. I compare lichens to Spanish moss (which is not a lichen but is a bromeliad) and think they enhance the garden.