Problem with admin_menu and Varnish
The error see to be on some cache file of drupal's admin_menu. The js aggregated file browser is requesting is being refused by Drupal by 503. You may get some pointers to this issue here https://groups.drupal.org/node/28604

Try clearing all the Drupal caches using "drush cc all" command. Are you using any js aggregation on Drupal side? Try changing to https://drupal.org/project/advagg?