Do I have to setup an MX record for our domain in order to run an SMTP server--all this is for is just emailing out?
No. MX resource records are for the rest of the world to find your SMTP Relay servers that listen for incoming SMTP Relay connnections from clients out of the rest of Internet, not for your SMTP Relay clients when they are talking to the rest of the world.
Do I have to open up port 25 to the outside world on an specific static IP for SMTP to work (or, perhaps to word it differently, is SMTP more than just a one-way street)?
No. You don't need to open up local port 25 at all. Your SMTP Relay client should use a port in the so-called "ephemeral" range. The remote port will be port 25, the well known port number for SMTP Relay servers.
Am I on the right track?
Yes. It sounds like you just need to find out why your spangly new Windows Server 2008 machine cannot make a TCP/IP connection to port 25 on 67.195.168.31, which is almost certainly a simple wrong-shape-of-hole-knocked-in-the-firewall issue. Although I suspect that you'll then find that Yahoo considers you to be a third-class Internet citizen that it refuses to have any dealings with. In which case: Welcome to the Balkanization of Internet SMTP mail! ☺
