Any insight as to why multiple Apple Mail IMAP accounts with Blackberry don't get emails? Thunderbird seems to work fine.

Question

I have two instances of Apple mail connected to the same IMAP server; one on my iMac and the other on my MacBook (when I travel).  I also have a Blackberry Storm connected to the same IMAP server.
The Blackberry gets emails fine.  The Apple Mail clients mostly don't get the same emails.  I have disabled the Blackberry and still get the same behavior.  Thunderbird or any web-based email client works perfectly well, so it seems the issue is with Apple Mail.
Anyone have any suggestions?
Frank G

Answer 1

If TCP port 25 isn't open, then SMTP services won't work.  That's the port that all SMTP servers use to communicate amongst themselves.    (Sure, you can change the port your SMTP server is listening on, but you'd also have to change the port processing on all of the other SMTP servers around — and if you did manage to implement that change everywhere, the local network folks would likely just block the new port for the same reasons they blocked the old port.)
If you have a public static IP address and have correct forward and reverse translations — host domain to IP address, and IP address to host domain name — then you don't need and very likely don't want to run your own DNS server. 
More to help you learn how these pieces fit together and not something I'd expect you would need given you have a public static IP and public DNS here is a detailed DNS server configuration article for OS X Server; enable Show All Records and it applies to Server.app on 10.7 and later.  If you have questions after reading that, I can certainly answer them and also update the article to try to reduce the confusion or answer the question.
Your host didn't have valid reverse DNS, so you'll want to get that cleared up, and you'll want to get the port blocks cleared, or work with the local network folks to set up a relay through one of the existing mail servers.