Google Wave is an extremely cool technology and Stack Overflow could be even better by integrating features from Google Wave. Add suggestions on what you think we could learn from Google Wave
Real-time collaboration is extremely cool, if disconcerting to start with. Obviously SO doesn't have the sort of resources (either human or machine) of the Wave team, but it would at least be interesting to have the option of making your answer visible to others as you were typing it.
I'd also love to be able to write a robot which could automatically link to bits of the .NET framework documentation or JavaDoc, but that sort of level of integration would be pretty tricky.
I think it's more likely that it'll be feasible to write a Wave robot to read and post to Stack Overflow... which may give at least some of the benefits.
The ability for thread to be marked as read or unread is extremely cool (discussion). The use of discrete green labeling to mark threads as unread is very nice. Spacebar in Google wave takes you to the next thing you haven't read (even taking you to another question if you were browsing a list). Something like that could allow me to review the answers to a question twice as fast.
The presence of a double organisation system - folders and tags is an extremely useful feature. Tags are basically what the community uses to organise, while folders lets a user organise questions themselves. I would like to organise the questions I've read in folders so that I could review them again later. Favourites are okay, but I don't think it scales so well