I have what I think is a similar, or at least related, problem.
I have a URL set up at dyndns.org. I'm hosting my Web stuff on my Cube. Localhost = 127.0.0.1, of course, and for other reasons I have my router pointing to my Cube at 192.168.0.51. My dyndns.org host is user.homeunix.net. I have an entry in my hosts file to point user.homeunix.net to 192.168.0.51.
I've installed WordPress in /WebServer/Documents/wordpress. When I go to http://user.homeunix.net/wordpress/, I get my blog whether I'm at home or out at some other client on the Web. Others can see my blog. It works fine.
But if I click on the blog title in the upper left of the main page (default template), it tries to take me to firstname-lastname-computer.local, which is fine on my LAN, but doesn't do much for anyone viewing the site from outside my LAN. When I rollover the title, the address bar at the bottom of Firefox tells me it'll take me to user.homeunix.net/wordpress, but I end up at my local host.
I have the DB_HOST set to user.homeunix.net in wp-config.php. In the admin settings in WordPress, the URI entries are set to user.homeunix.net/wordpress. I tried to add the trailing / to those entries, to no avail.
I'm not sure what I'm doing wrong, but it would be nice to try to get this ironed out. TIA!
EDIT: I should mention that I'm using MySQL 4.0.23 and PHP 5.0.2 on OSX 10.3.7. I had the "no page three" error when I installed WordPress initially, but I used phpmyadmin to go in and reset the admin password that way. Dunno if my problem might relate to lingering problems from that issue? Thanks again.