loop over all custom taxonomies for current custom post type and their values

You can make a loop to retrieve the taxonomies:

foreach( array('genre', 'rating', 'year') as $taxo ){
  #loop over each taxonomy
  $terms = get_the_terms( $post->ID , $taxo );

  if( $terms && ! is_wp_error( $terms ) ){
    echo $taxo . ': ';
    $myterm = array();
    #get list of term names
    foreach($terms as $term){
      $myterm[] = $term->name;
    }

   #display comma separated list of terms
   echo implode(',', $myterm) . '<br />';
  }

}

Functions used:

get_the_terms(),
implode()