Display custom field only if value present?

The easiest way would be to add a simple conditional:

$values = get_post_custom_values("listing_heading_10");

if ( $values ) { ?>
     <h3 class="listing-title"><?php echo $values[0]; ?></h3> 
<?php }

That said, is there any reason that you can’t put your output code in a foreach loop?

e.g.

$values = get_post_custom_values( 'some_value' );

foreach ( $values as $value ) {
     // echo output content here
}

It may be helpful to put your custom meta values into an array, to facilitate looping through them if they exist. So, instead of:

$values = get_post_custom_values("listing_heading_10")

…you could have:

$values get_post_custom_values( 'listing_heading' )

And instead of

$values

…you could output:

$values[10]

etc.