I have been trying to get Zimbra Admin working with konqueror here and have some info for you developers.
There are several occasions when starting up that konqueror complains about usage of window.getComputedStyle as an object, ie. in and the in ZaController, line 387, DwtBaseDialog, line 140. ZaController, line 219 and so on.
After this you don't even get a login prompt, only the Zimbra logo slightly too high on the page compared to the firefox display where the logo is centered.
I will see if I can find more info for you later on.