I went to Control Panel and un-installed Opera first and then downloaded the latest version and installed it. When I clicked on the link from an e-mail referring to this message, Opera came up with no problems. I then closed it and clicked on the desktop link and it came up OK, but still asked me if I wanted to make it my default and went through all the previous motions and still keeps asking me every time I start Opera from the task bar or desktop. It seems to work fine, but I cannot get rid of the message or get Windows to acknowledge any changes to the default Web Browser.
I really think Opera is reacting to the Windows issue of not showing any default browser, so it just asks me again, even though I tell it not to show the message any more.
So, I am still in the dark and think it is some kind of problem with Windows. Incidentally, I see the same thing on the Default Photo Viewer - it always shows the gray box with the + sign and I cannot change that either.