I've been using zimbra in a small company for some weeks now, and (like all changes) there are people who miss some of the features their old mail clients had.
One of the main concerns is about the spam filter. Sometimes junk mail is not the same for two users, one may consider something spam whereas another person might find it interesting.
So, you have a person who finds something interesting, and because two other people who have been receiving the same mail have marked it as junk, he gets the mail marked as spam automatically, even though he never marked it as such.
This can also happen the other way around, where a user gets mail he considers junk, from the same address, and he gets it over and over becuase other people don't consider it junk.
So, as a suggestion for future versions, I think the junk filter should be more flexible, and customizable for each user.
Aside from that, I have to say I'm very happy with the overall system.