Come on, you have to give us a little information if you expect help. Are all of your messages "invisible," or just some of them? Have you tested your acccount to see if it is working properly on your computer. [Send a message from a webmail account to the accounts that you access via Mail?]
If only some of your messages are "invisible," then they may be some type of badly formed SPAM. They may also be someone's mail server's less than perfect attempt to remove SPAM. I get a few messages like this at work. I also get a few of them on home home account. They show no sender, no recipient, no title, and no content. However, it never crossed my mind that Mail is the problem. My guess is that neither should you.
I think that my Mail has a real trouble. Sometimes I see messages. Other times I see nothing or I see some of the messages. I can see all the messages when I go to the boxes in Library and I open one by one.
And to close the application I have to "force quit". Nothing similar happens with Panther.
Thanks for the help, but I can't tell you more than I know.