You've got a couple of things going on here......the fungal growth on the dead limb is probably secondary; the limb was already dead before the growth appeared, as that type of fungal organism is most often present on dead/decaying wood. The growth developing on the healthy limb just looks like lichen, which is harmless, but I'd be concerned about the large bark split. That's not a good sign! And you need to know the reason the other limb died.

I'd contact a certified arborist to come out and diagnose the problems. Your extension service should be able to help you locate one or check the yellow pages for arborists. Make sure they are certified (initials CA or ISA after their name)!

Yet another Japanese maple cultivar with a dieback problem. Try searching forums for additional discussion, there has been lots over the years.