I like Opera, and wish them the best of luck with their business and their projects, but Unite doesn't change anything. It will be a barely used feature in a barely used browser.
Ever wanted to share all the photos/videos on your 120GB hard-drive? Unite does that too, bye-bye flickr.
Ever wanted to host online chat - it's already there in your browser now.
Ever wanted to listen to your music when all the files are on some other computer? Relay via Unite, it's in your browser.
Want to host web-pages on your local computer? Don't want to install a web-server .. no problem.
Really I find it awesome, I think we've only just scratched the surface here too. A genuinely new paradigm IMO, http://alicious.com/2009/opera-about-to-change-the-world/.
Welcome to the Peerweb.
Yes that is one of the down falls, pretty major too, but if you're family wants to share from your computer they can just call, or you can look and see the connections are 0 before turning it off. I can also imagine a caching/on-line backup system (like Dropbox) - eg for your fridge notes.
Peerweb is not the www they have a lot of overlap but this is going to change the way we use computers IMO.
Even ignoring the fact that the idea of "your computer" is becoming less and less a big box that sits on your desk and more and more a tiny device that you have in your pocket or your bag; and ignoring the fact that we'd really like for computers, even the big ones sitting on our desk, to sleep when not in use so we don't chew up so much power and produce so much waste; and forgetting about the fact that someone has to actually write the code for all of the magic functions to address the problems you've proposed Unite can solve (and for a proprietary platform that about 1% of users use); and discounting the chicken and egg problem that in order for this to be easily useful across all of your devices you have to have Opera on all of your devices. Even forgetting all of these, huge, probably insurmountable even to a company the size of Microsoft, problems, Opera Unite still doesn't solve any big problems that really effect users.
As far as "Welcome to the Peerweb." Wow, talk about drinking marketing Kool-Aid.
As far as a new paradigm is concerned .. not really. I think a new paradigm would be more like a rich technology that doesn't use the Web/HTML/HTTP at all.