Displaying custom field meta within WP_query loop

Your query should work if you call global $post and don’t reset the query (not needed when using WP_Query).

You can also try using tax_query.

$tax = 'issue';
$terms = get_terms( $tax );

   foreach ( $terms as $term ) :

echo $term->name;

 $args = array(
    'post_type' => $post_type,
    'post_per_page' => -1,
    'post_status'   => 'publish',
    'caller_get_posts' => 1
    'tax_query' => array(
             array(
               'taxonomy' => $tax,
               'field'    => 'ID',
               'terms'   => array( $term->term_id )
             )
           )
     );
 $my_query = new WP_Query($args); ?>

      <ul class="<?php echo $term->slug; ?>">
          <?php  if( $my_query->have_posts() ) : ?>

                <?php while ( $my_query->have_posts() ) : $my_query->the_post(); global $post; ?>

                            <li><a href="https://wordpress.stackexchange.com/questions/33064/<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>"><?php the_title(); ?></a> by <?php echo get_post_meta($post->ID, 'author', true); ?></li>

                <?php endwhile; endif; ?>

    </ul>

<?php endforeach; ?>

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