Take note, this loop will only work if the category is a single word. WP_Query requires the category SLUG in the loop. If the category name is two words or more separated by nonbreaking space, it will not work (I can verify that because I just tried it). I still haven't found a way to pull the slug from the given taxonomy term, but I'm working on it.
ADDENDUM:
Think I found a way to get around the multiple-word term name problem. Seems to work in my code.
<div id="content">
<h2 class="entry-title"><?php the_title(); ?></h2>
<div id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
<?php $terms = get_terms('YOUR_TAXONOMY_SLUG');
$count = count($terms); ?>
<?php if ($count > 0) {
foreach ( $terms as $term) { ?>
<h3><?php echo $term->name; ?></h3>
<ul class="taxonomy_group">
<?php $loop = new WP_Query(array('YOUR_TAXONOMY_SLUG' => $term->slug));
while ( $loop->have_posts() ) : $loop->the_post(); ?>
<li><a href="<?php the_permalink(); ?>"><?php the_title();?></a></li>
<?php endwhile; ?>
</ul>
<?php }
} ?>
</div><!-- #post-## -->
</div><!-- #content -->
Let me know if this works for anyone else or they see any holes in it.