Replication instructions:

1. Edit config.php and add

   $CFG->sessiontimeout = 10;

   This just sets a session expiry time of 10 seconds.

1. Log in and wait on the dashboard/site home for 10 seconds.
2. Now, click to expand either the messages or notifications menu in the header
3. Notice the exception popup, which doesn't provide the user with a whole lot of useful information.

Summary

When not logged in AJAX webservices return the error code servicenotavailable.
This is not a useful error code as it cannot be used to inform the user that they or not currently logged in.
I suggest a new error code of 'servicerequireslogin'

/lib/ajax/service.php

            if (!isloggedin()) {

                error_log('This external function is not available to public users. Failed to call "' . $methodname . '"');

                throw new moodle_exception('servicerequireslogin', 'webservice');

            } else {

                require_sesskey();

            }

This would obviously require a new language string for 'servicerequireslogin'