I'm using your module as a part of Wysiwyg Image Upload suit (thanks for great work!) and I needed to make the dialog window draggable.
So I added this line (89) to file jquery_ui_dialog_parent.js

$('.jquery_ui_dialog-dialog').draggable();

So the Drupal.jqui_dialog.create function now looks like this:

Drupal.jqui_dialog.create = function (options) {
    var self = this;

    // Note: We use scrolling="yes" for IE as a workaround to yet another IE bug
    // where the horizontal scrollbar is always rendered, no matter how wide the
    // iframe element is defined.
    var container = $('<div id="jq-ui-dialog-container"/>').append('<iframe frameborder="0" id="jq-ui-dialog-iframe" name="jq-ui-dialog-iframe"' + ($.browser.msie ? ' scrolling="yes"' : '') + '/>');

    $('body').append(container);
    self.container = $('#jq-ui-dialog-container');
    self.iframe = self.container.find('#jq-ui-dialog-iframe');
    // Open the jQuery UI dialog offscreen.
    self.container.dialog(options);
    // We need this for our theme to be in a namespace
    $('.jquery_ui_dialog-dialog').wrap('<div class="jquery_ui_dialog-dialog-wrapper"/>');
    $('.jquery_ui_dialog-dialog').draggable(); //make dialog draggable
  };

And it works for me.