What is the leatherlike, black stuff that has appeared in many bare spots in my lawn?
That material is most likely a mixture of ordinary moss and algae which has died and started to decay. Although growth of these plants is favored by wet, cool weather, they often begin to die when temperatures rise. Drying occurs during warm, windy days resulting in that black, leather-like product which you have observed. It often seems nearly waterproof. When dry, rake it up and dispose it. Correct any underlying soil and site problems associated with shade, drainage, compaction, and fertility.