How can I run a jQuery script in the admin overlay? I'd like to modify the interaction with one (or more) of my admin overlay pages, but it doesn't seem like the scripts that works on the site are directly functional in the back-end? How do I run a jQuery script within the Drupal admin overlay?

As you might tell, I'm quite new to Drupal.
You'll need to go in and do a form_alter on the admin overlay pages that you are wanting to modify. You will need to add an item to the ['#attached'] attribute on the form to attach your JS. You can read more about attaching JS to forms in the Drupal Form API documentation.