What an e-mail client sees is it's own particular view of the state of the mail store at the time. Actions taken by other clients that are simultaneously connected to the same account may not be reflected in other client views. For example, a deleted message may not actually be deleted until all other client connections disconnect. To insure that you are seeing the true state of the mail store at a time, make sure that you only have one client logged in at a time.
In addition, some clients (namely Outlook Express for instance) will totally ignore the existence of any message it thinks is malformed. Consequently you may see a message using the web client that a desktop client does not.