Well, I am starting to get a real understanding of why they made the UI decisions that seemed weird at first. I am even considering reading the specs and seeing if I get talk to their implementation of the server with my own client (to get things like growl/libnotify notifications working).
On the browser side, it seems to work best with Google Chrome. This is not a big shock. It doesn't seem as memory hungry with Google Chrome (63 MB vs 200 MB in Safari or Firefox on the first page), but it does seem to grow in size over time as I access waves (102 MB after accessing 10 waves). Another nice thing about Chrome is its model for tabs. Each runs in its own process, so killing a tab frees all of the memory associated with it. This means that when it starts eating too much memory, I can simply start a new Google Wave tab and close the old one instead of having to shutdown the whole application (which is what I have resorted to with Firefox and Safari). The downside is that Google Chrome has not been released for OS X. Luckily there is a developer version available for Linux and OS X (which is what I have been running).