After upgrading to Mountain Lion, one of my e-mail servers quit working on outgoing (SMTP) mail, saying it couldn't connect to the server. After some testing I found the solution on a forum which did work. In the outgoing server information which lists the servers and properties, set the one not working to "Custom" port and "25" as the port number, and not "Default" with the three listed ports.
It seems Mountain Lion changed something with Apple's mail where some SMTP servers won't work as before. Why it takes users to find the bug and solve the problem escapes me because it's an easy testable function that clearly the testing and debugging team failed.
And I can say that because I did this work for a number of years in data operations and management for the US Geological Survey. It's standard proceedure to test common things that worked to see they still work as before and expected.
For this Apple sucks on user friendliness to solve problems, but then after two updates to OS-X 10.8 there still are glitches which shouldn't be glitches. They were created than a result, which is why it sucks.