Check out pictures at link below.

Here is a link that might be useful: Azelea Pictures

The speckling is caused by an insect called the azalea lacebug. Not a real bad infestation....YET. The insects hang out on the under side of the leaves, somewhat disguised but they're there, if you look for them. There isn't anything else that causes speckling like that on the upper surface or black tar-like spots on the underside.

The problem with the branches could be one of two or three diseases that cause what is called 'die-back' . I have also seen these exact symptoms in the summer months after an extra cold winter. I don't know where you live in SC, but if it's in a location that doesn't usually experience really cold temperatures, and you got zapped like most of us did in the South, your plants could be experiencing bark splitting.