After upgrading to macOS Sierra and restarting my Mac, everything came up normally-except for Snapz Pro, a venerable screen-capture program that I had updated to the latest version (2.6.0), but should probably have disabled out of caution.
Snapz Pro launches at startup, but it’s supposed to hide itself without showing a screen. Instead, it had activated and locked one of my two displays. Clicking the red-dot close box on the Snapz Pro window didn’t help, and my second display was dimmed out, as if the capture window were in place. But clicking, pressing Escape, and other increasingly frantic actions did no good. I had a spinning rainbow over that screen, but the other was just fine.