[eric2006]

I have been trying to do this as well. The problem I have is that, if you make any changes to the library, they are only saved after you quit. So, if you add a song on one computer, then quit, it is saved, but if you have iTunes open on another computer at the same time and quit after that one, the new song will not show up in the library because the library index has been re-saved with the old version. If you only have one library open at a time, or quit on other computers before you make changes, you shouldn't have any problems. I haven't had problems listening to the same library file, without making changes
I'm not sure how the AirDisk works, but I resolved permissions issues on a firewire drive by doing "get info", then checking "ignore permissions on this volume" (on host computer). I can then mount the firewire drive on any computer over the network (the drive is connected to a G4 PowerMac w/ Gigabit), then open iTunes while holding the option key, and select the library on the external drive.
If your Mini has gigabit (or even if it doesn't), it may be faster to connect the drive to the mini - and you will need all the speed you can get. Gigabit switches are under $30 these days.