I've recently just installed Zimbra 3.0.1 on a fresh Fedora Core 4 install, and works fine, apart from being very slow at times, however I think this is due to the fact that I'm running this inside a VMWare server. I've assigned 1Gb ram to it, and a 10Gb partition for testing purposes.
The problem I see is that something appears to use up all of the memory on the box, and I see kernel messages displayed on the screen saying it's killing processes to make more memory, and finally dies when there's no more spare processes for it to kill. Reboot, and it comes back to normal, until it next occurs.
I've only had this installed for a day, but I've been able to reproduce this on two occasions now. I don't seem to need to put much load on the server either - I left the VM up overnight, came in in the morning and ran 'zmcontrol status' as user zimbra and it sat there doing nothing. A couple of minutes later I noticed the kernel messages being thrown up on the screen, and then locked.
Unfortunately, I don't have a copy of the messages here, but if anyone's interested, I could try to reproduce it and post what I see?
Apart from this though, it seems like a great piece of software!