Use named anchor in link of read more button

The l() function in Drupal 6 uses an $options array where you can pass a fragment.

'fragment' - A fragment identifier (named anchor) to append to the link. Do not include the '#' character.

To split the named anchor from your original URL you can use:

explode('#',$result->node_data_field_pager_item_text_field_url_value)

The code, including an if statement to check if the URL has a named anchor part,would become:

// add slide_read_more variable
if (isset($result->node_data_field_pager_item_text_field_url_value)) {
  if (stristr($result->node_data_field_pager_item_text_field_url_value,'#')) {
    $split_url = explode('#',$result->node_data_field_pager_item_text_field_url_value);
    $slider_items[$key1]['slide_read_more'] =  l('Read more...', $split_url[0], array('fragment' => $split_url[1],));
  } 
  else {
    $slider_items[$key1]['slide_read_more'] =  l('Read more...', $result->node_data_field_pager_item_text_field_url_value);
  }
}

Also have a look at the related how to: How to link Read more... button to another page instead of the node