So who's to blame, Opera or Twitter? Sounds like Opera to me if it worked in an older version but doesn't now (though I suppose if Twitter was doing something that was explicitly version specific, then Twitter would be to blame).
Well, this was very strange. All day I had to use Firefox to log into Twitter. Then Microsoft force-fed me the monster Windows update, I rebooted the computer - and all of a sudden I could log in with Opera. I never did get around to dealing with that Twitter widget!