I was pretty psyched about Wave myself. I got a semi-early invite (not the first batch, but within two months of its beta release). I also grabbed myself a copy of WaveBoard (OS X version) early on, which ameliorated some of the browser-based performance issues.
I fully agree with Stokes that its windowed UI was horrible. I don't think it's right to call it Windows 3.x style MDI though, as Win3.x was notorious for ridiculous overlap and overlap-clutter. Wave's problem is that more than 66% of the screen was NEVER being used 99% of the time.
I never had a problem with the live typing, because I am an awesome typist. It just made me look even more awesome.
Ultimately, the fatal flaw was that nobody used it. That's perhaps more of a result than a cause, but despite its UI weaknesses, I think I would have used it if people I knew used it more than once.
I think the whole closed beta and invite process was a mistake. When everyone was excited about it, virtually nobody could check it out. They squandered their peak moment of customer enthusiasm. If Wave had used this opportunity to establish some momentum, it might have carried it through.
It should have interoperated flawlessly with google chat. I know a lot of people who use google chat, and if I could have chatted with them using Wave, I might have done that. But as I said above (and as Jacqui said in her bit), nobody else used it. You would sign into Wave, and it's just you and the tumbleweed.
Finally, each time I logged into Wave, after weeks or even months, I didn't see any discernible improvement. I think when people saw it demo'ed, they were impressed but also left wondering how it was going to improve. People were expecting its featureset and/or functionality to grow, and not stagnate as some three-paned UI where you only use the third pane...receiving only performance updates. If Google wanted to keep it the same as it looked in beta, they were contributing to its doom.
Finally, and this isn't really anything Google could do much about, but I endeavored on a couple occasions to use it for work, but since info is being stored on a Google server somewhere, I found it too limiting what I could use it for. Some data I work is actually illegal to store offsite, so I couldn't paste that into a Wave.
I would love to see them try again....although now that they're going into cahoots with Verizon about privatizing the internet, maybe I'd rather see someone other than Google do it.