Within your LAN, you can telnet into your box's local IP port 110 and get your POP3 server to answer, correct? But when you try outside your LAN you don't get a POP3 banner? Are you telnetting into the same IP address when you do it from the outside, or do you have an inside and outside address? (i.e. 192.168.x.x/10.x.x.x and a real world IP address for the outside)
If you have two different addresses, do you have a router as a gateway to the Internet? If so, what kind is it, and do you have port 110 mapped over correctly?
You can interpret a lot of issues by looking at your /var/log/messages or /var/log/maillog (depending on your syslog configuration). POP3 sessions should be recorded properly in one of those files. If any connection attempt should be recorded.. even if you just telnet in and disconnect, you should get something like this:
Oct 30 10:41:54 l3det-phantom popa3d: Session from 127.0.0.1
Oct 30 10:41:55 l3det-phantom popa3d: Didn't attempt authentication