Some mail providers (for example Hotmail, AOL and GMail) will reject mail sent from servers running on dynamic IP addresses. It is possible to route such mail through your ISP's relay server whilst still sending most mail direct to the recipient server using MX DNS records.
Edit the relevant Mail Sender in the VPOP3 settings on the Mail Connectors tab. On the Settings tab for the Mail Sender in question you'll see a button marked 'Edit DNS Overrides'. Click on that and then add the appropriate overrides. For example:
hotmail.com smtp.myisp.com
would route all mail destined for addresses at hotmail.com through your ISP's relay server (smtp.myisp.com).
In VPOP3 version 3 and later, you can configure username/password settings as well
hotmail.com username:password@smtp.myisp.com