Deciduous azaleas are very hard to root. I would have a professional do it. You might contact Kathy Van Veen in Portland, Oregon. She has a service to root most rhododendrons and azaleas.

The one branch per year is a very arbitrary. A rule of thumb is to not remove more than 1/3 of the leaves in any season's pruning. Most azaleas will take more pruning.

There are several fungi that are common on azaleas:

Sooty mold growth on stems and petioles is a symptom of Azalea Bark Scale, Eriococcus azalea, and Cottony Azalea Scale, Pulvinaria floccifera. These small sucking insects feed on the bark and exude a sticky substance that turns the stems black. A scale infestation is indicated by sooty mold on leaves, yellowing of leaves, and twig dieback. This scale is most obvious from May through June when white egg sacs may be found in twig forks. Heavy infestations over several seasons may kill plants. Overwintering immature scales (nymphs) are about 2 mm long, gray, and are usually found in twig forks. This scale primarily attacks azalea and rhododendron, but has also been found on andromeda, maple, arborvitae, willow, poplar, and hackberry. Azaleas can tolerate low populations of this scale without injury, and if there are no yellowing leaves, no treatment is necessary. Beneficial predators and parasites will usually provide adequate control of light scale infestations. Examine egg sacs for holes which indicates control by parasites, and look for predators such as ladybird beetles. To control heavy infestations, spray dormant plants with a late oil spray to kill developing nymphs on twigs. If necessary a 2% summer rate of horticultural oil may be applied in July after all of the eggs have hatched.

A grayish white, powdery coating or fuzzy white growth on upper or lower surfaces is Powdery Mildew (Microsphaera azaleae). This is more prevalent on deciduous azaleas and sometimes it affects the lower surface more. Entire leaves can be covered. In late summer and fall, small black specks may be found in the white areas. Powdery mildew is more severe on shaded plants. It is favored by the high humidity found in crowded plantings and damp locations. The disease is more severe during periods of cool, moist weather. These fungi produce spores on the surface of the infected leaves which are spread by wind currents to surrounding leaf tissue. These fungi overwinter in the bud scales for initiation of infection next season. There are a number of ways to manage this disease.

Small bright yellow spots is a symptom of Azalea Rust, Puccininastrum vaccinii, a fungal disease. Orange-red pustules containing spores form on the lower surface of the leaf. This rust is only sporadically severe and typically infects deciduous azaleas. Control by avoiding those hybrids and species which are very susceptible to rust. Good air circulation is helpful. Triadimefon seems to help, but may not be registered for use on rhododendrons.

Here is a link that might be useful: Van Veen Nursery

Thanks for the primer, Rhodyman!

I guess there is nothing to do until things reappear this year on the leaves, but it doesn't sound EXACTLY like any of those, though perhaps it is Powdery Mildew and I've just failed to notice the early stages, and only caught it when it got to the black spots stage. (And come to think of it, its growth pattern does resemble the growth of mildew in a damp area of the house.)

I'd use Neem oil. Many sites sell it. This site describes it:

http://www.mooreandmoore.com/organics_pest.htm

Here is a link that might be useful: Moore&MooreWestOrganics