Have you tried re-indexing your mailbox? I haven't seen this particular issue, but lots of times re-indexing will solve weird quirks similar to that. You can re-index it through the admin console. You can open up your account and at the top there's a button for re-indexing the mailbox.
Another similar thing I've seen is Thunderbird will not cleanup drafts properly and in the web client it will show unread emails but list none. To fix that you go in to Thunderbird, right-click the Drafts folder and click Compact.
Also, welcome to the forums. We enjoy Zimbra too
