A popular theme, as expected, on Google Wave that I've noticed amongst a group of educators is the functionality of Wave.
Beyond the fact that it has bugs (slow, locking up), much discussion in the educator section (some found here) is how could Wave be used in the organizational setting.
Amongst the ideas: wikis, customer service, advising, and discussion boards.
A standard that is bubbling up is the number of people suitable to make a Wave useful. I participated in one Wave that had over 400 people, and it stopped just short of chaos. Early on participation in the Wave was robust, but after a very short time hundreds of messages can appear in the Wave, and it simply becomes impossible to keep up with. Hence, that Wave came to a grinding halt.
Talking about functionality at this stage of Wave is perhaps a bit moot as we begin to see bots, gadgets, and extensions being built for Wave. Just as the Twitter core was developed, Twitter did not gain a wider spread use until extensions, apps, and third party services tapped into its API (think Tweetdeck, Seesmic Desktop, Twitpic, etc...).
At current it appears many of the "Wave extras" are being built for the internal Wave.
As with Twitter, I'm curious to see how third party services extending the functionality outside of the Wave into websites and peripheral internet use will grow the idea of Google Wave: communication and collaboration.