I sounds like the plant was mistreated before you bought it and had been allowed to dry out.

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 over-winter in the bud scales for initiation of infection next season. There are a number of ways to manage this disease.

* Do not overwater or overfertilize plants, as the fungus prefers succulent new growth.

* Hand-pick and destroy mildewed leaves to control small amounts of infection.

* Hose diseased plants with water when practical. This can help remove fungus and prevent new infections.

* Prune and space plantings to allow good air circulation. Do not plant in extremely shaded or damp areas.

* Rake and destroy fallen leaves year-round to reduce infection source. Do not compost diseased materials.

You need to know what kind of an azalea it is. If it is a deciduous azalea, then it will probably overwinter OK if given some protection. If it is an evergreen azalea, then it is probably a house plant and should be brought in for the winter.

Azaleas have two very important requirements. They like acidic soil and very well drained soil. When grown outside it is good to mulch them since the roots are very shallow and do not respond well to weeds or weeding or wide temperature changes in winter or the heat of the summer sun. A mulch layer helps guard against these things.

Here is a link that might be useful: How to grow azaleas and their problems.

So, basically, as far as the mildew goes, I should hose it down and leave it be? I can't very well pick off the affected leaves. It would only have a few leaves left if I did that! The only problem I can see with that is gravity. Assuming this is a normal fungus, it will spread by spores...spores will be carried down by water...all the new, healthy looking leaves are at the bottom......where the spores in the water will fall right on them.....
It also sounds like if the plant makes it through the winter, the fungus will be back next year. Is there a way to kill it that does not involve toxic chemicals?
I tried to make the soil well drained by mixing some sand in the bottom soil of the planting hole. I also gave the plant some Miracid. It is mulched. Oh, it's in I guess a partial shade area. Full sun in morning, shade in afternoon.

If the plant is too bushy, opening it up will help. Rhododendrons need good air circulation to be healthy. They are not good hedge plants. They need to be somewhat open so they get good air flow through the plant.

Mildew comes from remaining damp.

If you hose them down, start at the top and work the way down and flush the new leaves well. Do this in the morning of a sunny day so that it can dry.

If you have a lot of shade, prune back the shade so that you get more light.

My azalea has white spots on the top side of the leaves, even on the new growth and rusty looking bumps on the underside of leaves. What could this be?

Whitish specks on the upper surface of leaves and dark spots varnish-like on the bottom are symptoms of Rhododendron Lace Bugs, Stephanitis rhododendri, and Azalea Lace Bugs, Stephanitis pyrioides, small insects with transparent wings on under-surface of leaves.. This insect hatches early in spring as the new foliage begins to mature and its numbers may build to damaging levels with successive generations. Lace bugs reach their peak in late summer and do their worst in sunny, exposed sites. Spiders are important predators of lace bugs and since they shy away from sunny, hot places, plant your azaleas where there is some shade. Insecticidal soap, horticultural oil, or a systemic insecticide may spare your azaleas the damage if applied in spring when the first hatchlings are noticed. Care must be taken to spray the lower surfaces of the leaves where the lace bugs live. Moving a plant to an area with more shade may alleviate the problem. Lace bugs are more prevalent on certain varieties. The following azalea cultivars have resistance to azalea lace bug: ´Dawn,´ ´Pink Star,´ ´Ereka,´ ´Cavalier,´ ´Pink Fancy,´ ´Dram,´ ´Seigei,´ ´Macrantha,´ ´Salmon Pink,´ ´Elsie Lee,´ ´Red Wing,´ Sunglow´ and ´Marilee.´

Here is a link that might be useful: How to grow azaleas and their problems.