I have been wrestling with this issue since last fall when 3.1.x came out.
The problem is NOT 10.5.7. The problem has to do with how the Mac account profiles are being handled. I can successfully launch Media Composer on the same Macs using the Windows OS, authenticating against the same server with Windows roaming profiles. I can also successfully launch Media Composer under the Mac OS if a local account is used rather than a networked account.
Looks like this is an Apple issue. A similar condition exists for Adobe Acrobat ver.9. The resolution for Adobe is a convoluted system of symbolic links.