@mike @sared, yes multisite. Point is that one sub-site works, other not. And the problem sub-site sometimes has the problem and sometimes not.
Perhaps a idea to force a full page redirect to the wp-login.php with the login data included when the 'undefined' shows up? I think its a good fallback solution that is more user friendly than a undefined message.
WP Super cache should also supports Ajax, but if we can find a bug there, I think we should locate it (just the Ajax response that confirms its that plugin), and report it to them. I think they would appreciate it :-)
Please let me know how you think about the fall-back solution above. Kinds regards, and keep up the good work! Sven