When using functions like add_submenu_page etc, make sure that you add them at the admin_menu action. If you try to add them any place other than that you will get “Insufficient Privileges” errors when trying to go to the page.
NOTE: If you are in WP 2.8 WordPress allows you to run those functions at admin_init, but don’t be fooled they will break again in WP 2.8.1.