I ran into the exact same issue today with an account. We're running 6.0.4.
I changed skins, cleared browser cache, closed/restarted the browser, messed with preferences, re-indexed the mailbox, etc...
I tried switching to the Standard HTML client which worked initially but after switching back and forth between different Zimbra tabs....it got screwed up as well. The Standard HTML client did give me a little box that said the client had run into a problem...but clicking on it did not give me any more info.
What DID work however...was running in debug mode. I was actually trying to get more info about what was going on, but as soon as I put it into debug mode...
http://HOSTNAME/zimbra/?debug=1
Everything came back as normal....and when I took it out of debug mode all was fine. Very strange.
This bug shows what the UI looked like for me...but we don't use the skin referenced in that bug...
Bug 43393 – Folders are not shown in left folder pane of email tab for some accounts
Matt