I just checked out the flash demo and read a little on the site. I just happened to be evaluating eGroupware when I heard about Zimbra, and _almost_ like Zimbra better except for one missing feature: resource booking. A module for booking meeting rooms, laptops, projectors, etc is an extremely useful feature.
I have a few more little "usuability" ideas. 1) It might be useful for the first time a user logs on, if they would be prompted to replace the Email link in the Windows XP start menu with a link to Zimbra. 2) Have a tray application much like the Gmail Notifier.
3) ...is a little more involved. Why need an extra client for offline access? Maybe there is some way to have a "local cache" of the Zimbra web interface (maybe not necessarily using firefox or IE, but maybe it would?), so users can also have the native Zimbra look and feel, even when offline!
Those are just my first impressions. With the power of AJAX, they seem to be possible.