Following is also not very flexible -- it doesn't appear to be possible to filter or group incoming updates except by selectively muting them, and you can't follow anyone other than a person with a Google profile.
(Google is already working to offset at least some of the negative feedback it's received on this score; the day after this article was written, the company announced some tweaks to its handling of followers, such as making followers and those you are following more visible and adding the ability to block followers.)
The most genuinely useful part about Buzz is how it works as an activity aggregator. Anything you post on YouTube, Google Chat, Flickr, Twitter or Picasa can be automatically funneled into Buzz. If you manage sites through your Google account's webmaster tools, you can siphon in feeds from those sites as well. However, this is a limited feature; for example, you can only add one Twitter feed (typically your own) through the "connected sites" link.
Note that there is some degree of privacy control for all of this: Individual posts can be marked as public or private, with "private" meaning one of a set of groups you define from your Google contacts list. (This is also useful if you want to direct messages to relevant audiences.) You can also choose not to feed a given site into Buzz at all.
The bad Buzz
Some things about Buzz are genuinely problematic.
Privacy problems. The privacy-protection features supplied by Buzz so far aren't broad enough. It's not clear how to enable disable geolocation features when posting from a mobile device, for instance. (Do you really want to tell people exactly where you are, all the time?) There are ways to disable it for individual posts, but it should be easier to change that feature on a general basis.
Your list of followers is another weak spot: It can't yet be subdivided into lists à la Facebook, but it can at least be made private via the Edit Profile page. Also, as mentioned before, some contacts you follow are chosen automatically, apparently based on your activity in Gmail with those people. None of this is impossible to fix, but it deserves attention sooner, not later.