To everyone experiencing the same problem, you can temporarily fix it by adding the following to the top of your wp-config.php file:
//temp fix for WP 3.5 not loading dynamic menus (jquery etc) define('SCRIPT_DEBUG', true);
Hopefully the WordPress team will come up with an official fix to this issue soon.
UPDATE: It seems that the problem was caused by the well-known BulletProof Security plugin and it has been fixed by the developer. Good job 😉