Why does iphone mail client show unread messages even though inbox is empty

Its an issue with POP mail accounts. The unread messages notifier at the bottom of the mail screen will not display properly unless the account is IMAP. Gmail once told me I had over 1 billion unread messages.

You can submit the bug to:
http://www.apple.com/feedback/iphone.html

Have you tried cleaning out your inbox on the server-side? I had this same problem and it turned out to be caused by a specific email I received -- as if it screwed up further processing of the inbox. Once I deleted the offending email, the proper number of messages in my inbox was reflected on the phone (and it hasn't happened since).

If you don't want to clean out your inbox, maybe you could create a temporary folder (server-side) and move all the messages from your inbox into this folder to see if it "fixes" the problem. Then you can move them back and try to figure out which one is causing the problem (if there IS a problem).

50? It shows mine as having 2,47,483,636 unread. Now I realise that there is a lot of spam out there, but I know I have never had that many emails. This is with a perfectly normal POP mailbox.

The same has happened to me in the past, and it has also shown -3 messages.