This is the same problem that this user has:
Mapi32.dll is corrupt or the wrong version
I haven't heard back from him yet, but I told him to delete the .idm file and try again.
I'm not exactly sure what is going on. I am hoping that 6.0.4 will resolve this, but I am not sure. I know that 6.0.2 has some install issues. I was hoping that this was bug 42644, since resolved, but I think this is a different problem.
I am curious -- on your machine can you search for all of the msmapi32.dll files and see their versions? I am especially interested in the one in Program Files\Common Files\System\MSMAPI\1033.
Another thing to try is to delete the Zimbra profile created during the install, and create a new one from scratch using the Mail Applet from the control panel. Then try to sync.
Let me know what happens.