Forced integration with Gmail. Buzz isn't a standalone item; it's part of Gmail, and that's the only way to access it right now. The mixture of metaphors -- mail vs. feeds -- is sometimes problematic. Example: You can "mute" (hide) individual Buzz items, both incoming and outgoing, with a click. Un-muting something, however, is a mess: You need to look in Gmail's Sent Mail folder (no, seriously), and you'll see a copy of the muted item which you can then unmute.
The biggest drawback, however, is that Buzz is essentially an extension to Gmail and not its own standalone item -- great for those of us who use Gmail regularly, but not so great for everyone else.
Difficult to decipher. Many settings and functions in Buzz are either not yet available or buried. The "mute" issue is one such thing; the link for editing connected sites also has a tendency to vanish without warning. If you want to give Google the benefit of the doubt, this could simply be early beta woes.
No API compatibility with Twitter or Facebook. Buzz's API is its own animal. Twitter's API is already widely embraced despite the system's relative youth, and for Google to shirk such potential developer leverage is just plain dumb -- especially since it lets you feed Twitter into Buzz, but not the other way 'round.
And Buzz doesn't work with Facebook at all, which could be an indication that Google considers it a rival. But let's face it -- Facebook is arguably the update venue that people use most. Right now, at any rate, it is unlikely that masses of people will be deserting the protected halls of Facebook for the more public (and confusing) Buzz arena. But it's also likely that some of them might like to post to both. By ignoring them, Google could be losing some potential users.
What's best about Buzz right now is how it puts a lot of things into one place. It could eventually turn into an extension of Google Reader, or rather, its opposite: Instead of syndicating content from the world at large, you're syndicating your own content stream for others.
This is valuable, especially since Google has a slew of disparate services -- both its own homebrew products and applications acquired from others -- which could be tied together more elegantly. Buzz might well be a way to do that.
The problem, again, is the implementation. Buzz feels a lot like Google Wave -- a few great ideas, all of them looking for a better way to be delivered.