I'm allergic to cats so after the second winter of vole damage, I mixed mouse poison in with the mulch. If the idea of poison bothers you, try setting traps. The other rather bizarre pestilence I've had to deal with is a regular infestation by what looks like cabbage worms. If not caught in time they can denude the azalea. A good dusting of Bt clears them up though.
Most azaleas are self-cleaning, meaning the spent blooms fall off.
However, the PJM varieties and some of the natives do need deadheading. Only prune you azalea to maintain a pleasing shape or to keep it under control. Prune right after blooming has ended. Azaleas set the next year's buds in the previous summer. Purchase your azaleas from a local nursery that specializes in shrubs.