How do I show a list of tags for the current category?

I think this will do what you want:

<?php
/* Retrieve all tags from posts in the current category */

$cat = get_query_var('cat');
//echo "<p>CAT:$cat</p>";

$sql = <<<EOSQL
SELECT DISTINCT t.*
FROM $wpdb->posts p
JOIN $wpdb->term_relationships tr ON p.ID = tr.object_id
JOIN $wpdb->term_taxonomy tt ON (tr.term_taxonomy_id = tt.term_taxonomy_id
       AND tt.taxonomy = 'post_tag')
JOIN $wpdb->terms t ON tt.term_id = t.term_id
WHERE
   p.ID IN (
      SELECT p2.ID
      FROM $wpdb->posts p2
      JOIN $wpdb->term_taxonomy tt2 ON (tt2.term_taxonomy_id = $cat)
      WHERE p2.post_type = 'post'
      AND p2.post_status = 'publish'
      AND p2.post_date <= NOW()
   )
EOSQL;

$terms = $wpdb->get_results($sql);

// print_r($terms);

echo "<br />";
foreach ($terms as $term) {
   echo "ID:$term->term_id NAME:$term->name SLUG:$term->slug<br />";
}

?>