order

If you make a Files view a draggable view, with an integer field and using the FieldAPI handler, everything looks great except for this error:

Undefined property stdClass::$nid in draggableviews_handler_fieldapi->get() draggableviews_handler_fieldapi.inc

and the fact that it doesn't work at all.

AJAX sorting of book pages is built into Drupal's book module.

Navigate to Content Management » Books » List, and click "edit and order titles" for the book you care about.
admin/content/book/[nid-of-book-parent]