It seems there's a CSS collision with .ui-front between CiviCRM's modal dialog boxes and the Drupal media module. CiviCRM seems to use inline CSS to set the z-index property on its dialogs. This didn't do any harm until a recent fix for Media dialog appears underneath the Ctools modal dialog when using jQuery UI 1.10 now defines media's .ui-front as !important and CiviCRM's inline style is no longer able to update the z-index. This issue essentially makes CiviCRM unusable for anyone using the media module or Drupal distributions built with media (e.g. a lot of them.)
I believe this can be most easily fixed by moving the style for CiviCRM's .ui-front from inline to a CSS file and using a more specific selector to set the z-index for the modal dialogs. This should get around the !important declaration on media's .ui-front z-index setting.
In the meantime, users of the media module may need to manually edit the media/css/media.css file to remove the !important tag from the .ui-front z-index property.