I am also having problems with the Custom Menu with Twenty Twelve theme. Fortunately, my blog is not yet public. However if these problems continue I will need to drop either the theme or wordpress.com.
Most of my menu structure has disappeared, and when I try to re-instate some portions of the structure, there is something that breaks after a few updates. I have the impression that the problem is related to the code associated with wordpress.com/wp-admin/nav-menus.php.
And, the attempt at humor in the 503 Error message (seen 6 times in the last hour) is wearing thin: "Goshdarnit! Something has gone wrong with our servers. It’s probably Matt’s fault. We’ve just been notified of the problem. Hopefully this should be fixed ASAP, so kindly reload in a minute and things should be back to normal."
Seeing that message too many times leads to a serious crisis of confidence in wordpress.com and .org.