Thanks guys. I should have done some digging via Google first, but I was a little freaked out. Poor mutt. He's a gorgeous dog, and I'm horrified that his owner has let him suffer with whatever it is for so long. His whole back is a mess.
I guess it was premature for me to call it "mange", but that's what comes to mind when a dog's hair is falling out and its skin is all scabby. Unfortunately it looks like there aren't any pills I could sneak to him, and I have no way of communicating with the owner (my Mandarin is limited to about a dozen words). Besides, if she's allowed it to get this bad, she obviously doesn't care.
I have a small "rash" on my wrist now, so I'm guessing I got something from him. Could be coincidence, but. . . . Oh well. It looks like sarcoptic mange is contagious but lasts only about three weeks in humans, because the mites can't live on us. And as Botch wrote, the other type won't even do that much. So at worst it's a few weeks of annoying itching.
Thanks, especially to Botch, liber45, and Noname, and sympathies to you, Pangea; that would be awful.