There is a Google Wave extension that has finally made the use of Wave for project management somewhat feasible. Unawave is a service that allows you to create projects, milestones, and tasks within the Google Wave ecosystem. Unawave automates keeping track of details in your project. You even get a dashboard Wave so that you can oversee the whole thing at a glance.
Google Wave is now just over one year old. While many of us geek types ooohhed and aaahhed over the new things that Wave could do, when first announced, we were disappointed with how flat Wave fell on its face due to low adoption. Much of this was caused by the relatively few numbers of invitations available. It's not surprising that using Wave for managing projects was simply undoable. There would always be somebody who could not get in. Even if they did, they were confused by Wave itself.
That has changed now that Google Wave has opened up to everybody. In my current experience, I am starting to see greater adoption of the service; I'm also pushing it on others so that they are at least familiar with it. I intend to use Unawave for managing my personal and work projects.
The advantages of using Wave are that you can add other people to a discussion, you can have private conversations, you avoid emails crossing in the ether, and most importantly, there has been no mention of file storage limits, which most project management services charge a premium to use.
Unawave is still relatively new. It is also another layer of complexity on top of the complexity of Google Wave itself. However, it does lend some structure to the chaos. I'm hoping that the structure from Unawave is sufficient to mask the mess that Wave can become. In other words, it keeps individual Waves on task rather than turn into the series of rabbit hole discussions that typically result.
Obviously, there are shortcomings to using Unawave and Wave. The lack of mobile clients means that you must have your computer nearby at all times to use the services. Another disadvantage is that they can be damned confusing to anybody who has never used project management software before, and who gets confused with basic email.
When Wave was first announced, one of the first questions asked was, "what problem does Wave solve?"
The answer has always been the need for more efficient collaboration. The wide range of uses of Wave ensured that it could never solve any one problem. Adding Unawave, however, at least gives users a path to follow for collaboration, which Wave could always do natively anyway. Think of Unawave as training wheels for Wave. Over time, you may find that you can stay on task on your own.