More: although I have unchecked the "Require password to stop" for the screensaver, if the screen remains locked (and the computer sleeping) for a few minutes, I get the same double-window problem. I have the screensaver to kick in after 3 minutes, so maybe the screensaver is launching right after waking up the computer if it has been 'idle' for longer than the 3 minutes, and this refreshes the screen or something? It's really puzzling.
More: although I have unchecked the "Require password to stop" for the screensaver, if the screen remains locked (and the computer sleeping) for a few minutes, I get the same double-window problem. I have the screensaver to kick in after 3 minutes, so maybe the screensaver is launching right after waking up the computer if it has been 'idle' for longer than the 3 minutes, and this refreshes the screen or something? It's really puzzling.