As far as the content goes...
... I can't figure out what niche Buzz is trying to fill, exactly.
The best thing I can describe it as is a friends-only Twitter with an RSS reader for other social networking mashed into it; this immediately highlights it's major problem, which is that Twitter is so successful because it's open and searchable and browsable and hashtaggable and RTable and all that other chaff that makes up Twitter... which Buzz doesn't have. Okay, it's nice to have no character limit and the ability to do simple threading, but where's my searching for zeitgeist topics, where's my ... searching at all? This is Google, isn't that kind of their speciality? As it is you're just shouting out into a group of people you could reach via gchat, wave or even just plain old email already. All it's doing is speeding up cc:s.
It's also nice to be able to automatically get people's twitter feeds or blog posts from other sites automatically fed into it... this is still no more useful than an RSS feed, however, because you can't post back to those original sources. It's like saying to someone 'well, I'll listen to you shout across this field but when I want to reply you'll have to walk over to me'. The lack of multi-threading may be an issue if it ever gets high-volume posts going, because it means everyone's replies will just be in one blob rather than making more coherent ordered sense.
And of, course, any of my friends who care about micromessaging or status updates like this have a twitter anyway, so they don't care about it... Ultimately, about the only thing it's got going for it right now is the fact it's right there in your email window.