I wish to possess a page that shows all posts, separated by category. The concept is to buy the groups, after which iterate through all posts for every category. The issue is complicated because I wish to iterate through all posts of the given custom type, utilizing a custom taxonomy because the groups. (Running Wordpress 3)

During my functions.php, my custom publish type is registered as "video" and also the custom taxonomy as "video_types".

During my custom page template that's designed to show all videos arranged by category, this is actually the code that is not coming back any posts (and they are there, I checked):

<?php 
  $categories = get_categories(array(
    'taxonomy' => 'video_types'
  )); 
  foreach ($categories as $cat):
?>
 <section id="<?php $cat->slug ?>" class="video-category">
     <?php
  query_posts(array(
      'cat' => $cat->cat_ID,
      'posts_per_page' => -1
         ));
     ?>
     <h2><?php single_cat_title(); ?></h2>
    <p class="description"><?php echo category_description($cat->cat_ID); ?></p>
  <?php while (have_posts()) : the_post(); ?>
      <?php
       $category = get_the_category(); 
            echo $category[0]->cat_name;
      ?>
      <div id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
      <article class="video">
        <h3><?php the_title(); ?></h3>
        <p>
          <?php the_content() ?>
        </p>
      </article>
  <?php endwhile; ?>
 </section>
<?php endforeach; ?>

Jeez, when you determine that every item of the custom taxonomy is known as a phrase (not immediately apparent within the wordpress paperwork for that noob), its all easier to find. This option would be simpler to know without all of the custom query stuff.

<?php
// A term is an item of a taxonomy (e.g. "Promotional" could be a term for the taxonomy "video_type")
// ...so $categories could be $terms and it would still make sense
$categories = get_terms('taxonomy_name'));
foreach( $categories as $category ):
?>
  <section class="category-<?php echo $category ?>">
    <h2><?php echo $category->name; // Print the cat title ?></h2>
    <p class="description"><?php echo $category->description ?></p>
    <div class="<?php echo $category->post_type ?>-list">
      <?php
      //select posts in this category (term), and of a specified content type (post type) 
      $posts = get_posts(array(
        'post_type' => 'custom_post_type_name',
        'taxonomy' => $category->taxonomy,
        'term' => $category->slug,
        'nopaging' => true, // to show all posts in this category, could also use 'numberposts' => -1 instead
      ));
      foreach($posts as $post): // begin cycle through posts of this category
        setup_postdata($post); //set up post data for use in the loop (enables the_title(), etc without specifying a post ID)
      ?>
        // Now you can do things with the post and display it, like so
        <article id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
          <h3><?php the_title(); ?></h3>
          <?php 
            // Getting custom field data example
            echo get_post_meta($post->ID, 'field_key', true); 
          ?>
          <?php the_content() ?>
        </article>
      <?php endforeach; ?>
    </div>
  </section>
<?php endforeach; ?>

And then for any gaps to understand could be filled by searching the functions above within the wordpress codex. Within the above code, for my specific application, custom_publish_type_title could be video, and taxonomy_title could be video_type (or video_types, I forget).