The problem appears to be related to a bug in user name recognition. Apple has published a KB article dealing with the issue. The problem seems to be triggered if your member name is in mixed case, or if it is in all caps. MobileMe requires the user name be in all lower case letters, although the same rule does not apply to passwords.
Apple suggests you go to your iPhone settings, and under account info make sure your name is all lowercase. If not, a visit to the KB article would be advised. The fix is simple: just delete and re-enter your account details, getting your member name in a form Apple will like. When the bug is fixed, this workaround won't be needed.
Apple needs to continue to pay close attention to MobileMe. My perception is it has become generally more reliable since the ugly launch in 2008, but the support page still reports a few new glitches per week. Lately I've noticed a few mail outages/slowness and difficulty getting to my iDisk.