I checked the zone file for tlthost.net and removed the line with localhost. I don't even remember why I tried that. I'v also ordered a book on DNS and BIND. I think I need it.
It seems that I can send and receive to the admin@ address from and to everywhere now. I'm only getting one error when I check http://member.dnsstuff.com/pages/dnsreport.php
Duplicate MX records
WARNING: You have duplicate MX records. This means that mailservers may try delivering mail to the same IP more than once. Although technically valid, this is very confusing, and wastes resources. The duplicate MX records are:
www.tlthost.net. and mail.moultonboro-nh.com. both resolve to 18.104.22.168.
I can't seem to find where I went wrong to get that, but I guess that's better than nothing.