I trashed TextEdit's plist and restarted...with no joy, and I followed that with trashing TE's cache (Edit: and restarting), also with no joy.
I just discovered that even opening a new TE doc calls up the password dialog box, but it only takes two "Cancels" as opposed to the four it takes to open a populated doc.
Weirder and weirder!!!
It's doing this when it attempts to fill the Open Recent menu. Run TextEdit, click the File menu, go to Open Recent, and choose Clear Menu from the bottom.
