Generally sounds like some sort of preferences issue to me. (Create a test user if you don't have one, add an E-Mail account to Mail.app and see whether the problem appears there, too.) If, as I suspect, the test user would be fine, I'd go about removing preference files for Mail.app. The most obvious one is ~/Library/Preferences/com.apple.mail.plist – I'm not sure what is all contained in this one file. Make sure to make a backup before deleting files.
Thanks Fryke. I have followed your suggestions and I'll see how it all pans out. So far my historic emails that spread out horizontally from here to the distant horizon are still in my inbox, but I'll keep an eye on it!