Dagnab it. Somehow the content on my Zune hard drive seems to have gotten fouled up.
So, I renamed the two folders on my PC where I store my Zune music. Then I cleared the contents off the Zune (with the Zune software). Then I changed the two folders back to their original names, and I'm re-syncing everything.
It's taking a while, given the number of songs I had on there, but when I'm done I hope all will be as it should.