I was finally able to finalize the migration of one of my clients to Google's "Apps for Businesses" last night!
When discussing the particulars, it came to light that one of the user accounts kept getting an error message from Microsoft Outlook:
"Your IMAP server wants to alert you to the following: Web Login Required:"
Huh? Why would an IMAP server tell an Outlook server that they needed a web login?
I still don't know the cause, but based upon the "answer" provided by Google, I suggested the user solve a CAPTCHA provided by Google. That solution didn't make really make sense to me, and it didn't resolve the problem.
After that failed, I suggested the user reset their password, which was also provided as part of Google's answer to this issue.