Get the title of the active tab
menu_get_active_title() should be the function you are looking for.

function menu_get_active_title() {
  $active_trail = menu_get_active_trail();

  foreach (array_reverse($active_trail) as $item) {
    if (!(bool) ($item['type'] &amp; MENU_IS_LOCAL_TASK)) {
      return $item['title'];
    }
  }
}


It should work for menus for which the menu type contains the flag MENU_LOCAL_TASK (which includes also the MENU_DEFAULT_LOCAL_TASK menu type).

The function is also defined in Drupal 7.

Update: I noticed that for menus like /node/%node/view, menu_get_active_title() returns the title for /node/%node.
The following code should return the correct title also in those cases, including in the case the title is given by a title callback. I just tested on Drupal 7; I don't actually have Drupal 6 on the test site I use.

$item = end(menu_get_active_trail());

if (!empty($item['title_callback'])) {
  $args = array();
  if (!empty($item['title_arguments'])) {
    foreach ($item['title_arguments'] as $value) {
      if (is_int($value)) {
        // Get the value from the menu item map.
        if (!empty($item['map'])) {
          $args[] = $item['map'][$value];
        }
      }
      else {
        $args[] = $value;
      }
    }
  }

  $title = call_user_func_array($item['title_callback'], $args);
} 
 else {
   $title = $item['title'];
 }