Show 1 product from each category

It looks like you’re mixing blog terms with woo terms but you may get a better answer at the woo support area.
PS: Put code in between backticks – otherwise it can get magled.

I use the following code to list all “categories” of the “product_cat” taxonomy. So, I assumed I would be able to also use to blog terms to display the categories of the product_cat taxonomy?

<?php
//list terms in a given taxonomy using wp_list_categories (also useful as a widget if using a PHP Code plugin)

$taxonomy     = 'product_cat';
$orderby      = 'slug';
$show_count   = 0;      // 1 for yes, 0 for no
$pad_counts   = 0;      // 1 for yes, 0 for no
$hierarchical = 1;      // 1 for yes, 0 for no
$title        = '';

$args = array(
  'taxonomy'     => $taxonomy,
  'orderby'      => $orderby,
  'show_count'   => $show_count,
  'pad_counts'   => $pad_counts,
  'hierarchical' => $hierarchical,
  'title_li'     => $title
);
?>
<div style="font-size:20px;float:left;margin-top:22px;"><span style="color:#E77738;">Best Selling</span><span style="color:6c6c6c;"> Products</span></div>
<ul id="products-grid-categories-list">
<?php wp_list_categories( $args ); ?>
</ul>

By the way, here is my code in question more organized:

<?php
$taxonomy = 'product_cat';
$orderby = 'slug';
$show_count = 0; // 1 for yes, 0 for no
$pad_counts = 0; // 1 for yes, 0 for no
$hierarchical = 1; // 1 for yes, 0 for no
$title = '';
$empty = 0;

$args = array(
//'taxonomy' => $taxonomy,
'orderby' => $orderby,
'show_count' => $show_count,
'pad_counts' => $pad_counts,
'hierarchical' => $hierarchical,
'title_li' => $title,
'hide_empty' => $empty
);
?>
<?php $all_categories = get_categories( $args );
  foreach($all_categories as $category) {
      $posts=get_posts('taxonomy=product_cat&hierarchical=1&showposts=1&cat='.$category->term_id);
      if ($posts) {
        echo '<div id="'.$category->slug.'"><p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>'.$category->name.'</a> </p> </div>';
        foreach($posts as $post) {
          setup_postdata($post); ?>
          <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
          <?php
        } // foreach($posts
      } // if ($posts
    } // foreach($categories
?>