Are you on the latest version available from the members area?
Are the domains receiving mail all on the same server / domain as ListMail? Often, if there is an authentication / relaying problem local messages will get through but remote ones won't.
All I can really recommend is that you double check your SMTP authentication username and password. You could also try "localhost" as your SMTP host with no additional authorization. Be sure your "bounce to address", on the Config page, is set to an address on your ListMail domain. Also, on some very restrictive hosts, you may only set the "bounce to address" and "send from email" (for each list) to an existing mail account on your server.