How to Reload the Dashboard After Clicking Update in Quick-Edit?

We have to intercept the Ajax end point of that action. The file wp-admin/admin-ajax.php has all the possible hooks in the $core_actions_post array.

The function wpse_65157_ajax_inline_save() is a copy of the Core’s, with a “force reload” script printed at the end. It has to be with Javascript, as wp_redirect() doesn’t work.

add_action( 'wp_ajax_inline-save', 'wpse_65157_ajax_inline_save' , 0 );

/**
 Copy of the function wp_ajax_inline_save()
 http://core.trac.wordpress.org/browser/tags/3.4.2/wp-admin/includes/ajax-actions.php#L1315

 Only Modification marked at the end of the function with INTERCEPT
*/
function wpse_65157_ajax_inline_save()
{
    global $wp_list_table;

    check_ajax_referer( 'inlineeditnonce', '_inline_edit' );

    if ( ! isset($_POST['post_ID']) || ! ( $post_ID = (int) $_POST['post_ID'] ) )
        wp_die();

    if ( 'page' == $_POST['post_type'] ) {
        if ( ! current_user_can( 'edit_page', $post_ID ) )
            wp_die( __( 'You are not allowed to edit this page.' ) );
    } else {
        if ( ! current_user_can( 'edit_post', $post_ID ) )
            wp_die( __( 'You are not allowed to edit this post.' ) );
    }

    set_current_screen( $_POST['screen'] );

    if ( $last = wp_check_post_lock( $post_ID ) ) {
        $last_user = get_userdata( $last );
        $last_user_name = $last_user ? $last_user->display_name : __( 'Someone' );
        printf( $_POST['post_type'] == 'page' ? __( 'Saving is disabled: %s is currently editing this page.' ) : __( 'Saving is disabled: %s is currently editing this post.' ),    esc_html( $last_user_name ) );
        wp_die();
    }

    $data = &$_POST;

    $post = get_post( $post_ID, ARRAY_A );
    $post = add_magic_quotes($post); //since it is from db

    $data['content'] = $post['post_content'];
    $data['excerpt'] = $post['post_excerpt'];

    // rename
    $data['user_ID'] = $GLOBALS['user_ID'];

    if ( isset($data['post_parent']) )
        $data['parent_id'] = $data['post_parent'];

    // status
    if ( isset($data['keep_private']) && 'private' == $data['keep_private'] )
        $data['post_status'] = 'private';
    else
        $data['post_status'] = $data['_status'];

    if ( empty($data['comment_status']) )
        $data['comment_status'] = 'closed';
    if ( empty($data['ping_status']) )
        $data['ping_status'] = 'closed';

    // update the post
    edit_post();

    $wp_list_table = _get_list_table('WP_Posts_List_Table');

    $mode = $_POST['post_view'];
    $wp_list_table->display_rows( array( get_post( $_POST['post_ID'] ) ) );

    // INTERCEPT: Check if it is our post_type, if not, do nothing  
    if( 'post' == $_POST['post_type'] )
    {
    ?>
        <script type="text/javascript">
            document.location.reload(true);
        </script>
    <?php       
    }
    // end INTERCEPT

    wp_die();

}

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Reference Q&A: How to enable comments for pending and draft posts?