I've had several users report this to me (IE 6/7 on WinXP) and I've occasionally seen it myself (FF 2.0 on FC6). When you delete a message in the Zimbra Web Client the message does not disappear from the view. If you change to a different folder and come back to the folder you were working in the message is gone, so the delete is in fact working, but the delete is not immediately reflected in the view.
I found bug 13989 which seems to address this issue. However, the bug is marked as unconfirmed and there were no updates on it since January, until I added a comment yesterday. I don't know how I could possibly post screen-shots or anything like that to prove the problem exists, but I have seen it with my own two eyes.