I have installed Zimbra Desktop 7.2 on my Linux desktop (Kubuntu 12.04 64bit) and it work's fine when I start Zimbra via desktop icon. In KDE system settings I added autostart for Zimbra and it starts but this never comes to an end. I do use exactly the same command for autostart as is used by the desktop icon:
"/opt/zimbra/zdesktop/linux/prism/zdclient" -webapp "/home/user/zdesktop/zdesktop.webapp" -override "/home/user/zdesktop/zdesktop.webapp/override.ini" -profile "/home/user/zdesktop/profile"
I did the same on my 32bit Kubuntu 12.04 netbook and autostart works fine.

I have installed the following Java versions:

On my desktop (autostart doesn't work):
java version "1.7.0_21"
OpenJDK Runtime Environment (IcedTea 2.3.9) (7u21-2.3.9-0ubuntu0.12.04.1)
OpenJDK 64-Bit Server VM (build 23.7-b01, mixed mode)

On my netbook (autostart is working):
java version "1.6.0_27"
OpenJDK Runtime Environment (IcedTea6 1.12.5) (6b27-1.12.5-0ubuntu0.12.04.1)
OpenJDK Client VM (build 20.0-b12, mixed mode, sharing)

Anybody who has got a clue?