wordpress simple loop, huge issues

by

Add wp_reset_query(); after your loop to prevent other loops on the page (for example, the navigation) to break.

<?php 
    query_posts( array ( 'category_name' => 'left_sidebar', 'posts_per_page' => 4, 'orderby=menu_order' ) );
    if ( have_posts() ) : while ( have_posts() ) : the_post();
?>

<li><a href="https://wordpress.stackexchange.com/questions/84336/<?php the_permalink();  ?>"><?php the_title(); ?></a></li>

<?php
    endwhile; endif;
    wp_reset_query(); // reset query
?>

Does this also fix your other problems?

reference: http://codex.wordpress.org/Function_Reference/query_posts#Usage