I thought Mountain Lion would resolve this particular issue, but it persists. I have an iMac. My wife and I have accounts on the computer and on iCloud. She can enable Back to My Mac. I cannot, even if her account is not enabled for Back to My Mac. I have tried to enable mine first after a reboot. But no matter what I do, it says the server responded with an error.
iMac, Mac OS X (10.7.2), Late 2010