WordPress update failing
Are there any more error messages, probably also in the servers log files? Probably the download for the update should be done to /tmp and you are not allowed to store files there? Try setting the constant WP_TEMP_DIR which should change the directory. Put something like this in your wp_config.php:
define('WP_TEMP_DIR', ABSPATH . 'wp-content/');
The permissions you're using seem reasonable, but they will only work if the FTP user that WordPress is using (set in your wp_config.php file) is the same as the owner of those files/folders.