If you move /admin to a separate menu, you loose the breadcrumb since it's not in the active menu. This module offers a turnkey solution - instead of this module you could also create a a custom menu with Menu module, move your admin links there, and customize in a site-specific module the hook_init code here with that menu name. Note, breadcrumbs will still break if the first part of the path is not 'admin'.

The .info file:

; $Id$
name = "Admin menu block"
description = "Moves the /admin menu ito a separate block, while keeping breadcrumbs sane."
package = "Administration"
core = 6.x
dependencies[] = menu

The module file:

// $Id$

/**
 * @file
 * Renders the admin menu in its own block
 */

function admin_block_enable() {
  drupal_set_message(t('You must now visit the !url page to enable the new block and see your admin links.', array('!url' => l(t('Blocks'), 'admin/build/block'))), 'warning');
}

/**
 * Implementation of hook_init().
 *
 */
function admin_block_init() {
  if (user_access('access administration pages')) {
    if (arg(0) == 'admin') {
      menu_set_active_menu_name('admin-block');
    }
  }
}

/**
 * Implementation of hook_menu_link_alter().
 *
 */
function admin_block_menu_link_alter(&$item) {

  if (empty($item['customized']) && $item['module'] == 'system') {
    if (strpos($item['link_path'], 'admin') === 0) {
      $item['customized'] = 1;
      $item['menu_name'] = 'admin-block';
    }
  }
}

The .install file:

// $Id$

/**
 * Implementation of hook_install().
 */
function admin_block_install() {

  $t = get_t();
  if (db_table_exists('menu_custom')) {
    db_query("INSERT INTO {menu_custom} (menu_name, title, description) VALUES ('%s', '%s', '%s')", 'admin-block', $t('Administration'), $t('The administrative links are put here by the admin_block module.'));
  }
}

/**
* Implementation of hook_uninstall().
*/
function admin_block_uninstall() {

  $result = db_query("SELECT * FROM {menu_links} WHERE menu_name = '%s' AND depth = 1", 'admin-block');
  while ($item = db_fetch_array($result)) {
    if ($item['module'] == 'system') {
       menu_reset_item($item);
    }
    else {
      $item['menu_name'] = 'navigation';
      menu_link_save($item);
    }
  }

  db_query("DELETE FROM {menu_custom} WHERE menu_name = '%s'", 'admin-block');

  db_query("DELETE FROM {blocks} WHERE module = '%s' AND delta = '%s'", 'menu', 'admin-block');
}