Same problem here. Mail, connecting to an Exchange was initially working fine on an iMac that I upgraded to Mountain Lion, and also worked on my iPhone and iPad. A few hours later I started getting a dialog box that my password was incorrect. Mail continued to work fine on iPhone and iPad, as well as on my home computer. server,
This morning I was still getting the error and when I tried to log in to the Exchange web client it failed there too. It turned out that my account had been locked, presumably because my work computer is sending the incorrect password. I unlocked the account, changed the password on the computer, iPhone, and iPad and was able to retrieve mail on all three. 15 minutes later I got the incorrect password dialog again on the ML computer, but the iPhone and iPad continue getting mail for about 30 minutes, at which point the Exchange account was locked again.
Seem as though this could be a keychain problem, though it's very odd that it only happens with Exchange.