Why would I get a 404 on "Authoring Information" autocomplete? Below is a screenshot of a 404 I'm receiving on the standard author autocomplete, and I can't figure out, for the life of me, why this would be happening.
Most likely because your autocomplete isn't actually using the standard path for the user autocomplete.

From the image, your autocomplete is pointing to /login/autocomplete, a path that doesn't exist in a standard Drupal installation (or indeed one with about 200 contrib modules enabled, I just grepped a couple of large projects).

The correct path for the user autocomplete is /user/autocomplete.

Presumably there's some custom/contrib code changing the autocomplete to a different path, but failing to actually implement that path.

The best thing to do would be to search your codebase for the string login/autocomplete and go from there.

UPDATE

The change might be being made by the User Tweaks module:

function user_tweaks_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  if (user_access('view login autocomplete')) {
    switch ($form_id) {
      case 'user_login_block':
      case 'user_login':
      case 'user_pass':
        $form['name']['#autocomplete_path'] = 'user/login/autocomplete';
        break;
    }
  }
}