Shindig-Integrator provides its own (compressed) copy of jQuery 1.3 in js/jquery.all.js. The file is included with drupal_add_js() in theme_add_gadget().
Drupal already provides a (compressed) copy jQuery 1.2.6 in misc/jquery.js. Drupal and most of the modules are written to work with jQuery 1.2.6 not 1.3.
Once a gadget is included on a page, Drupal's jQuery is replaced by Shindig-Integrator's one. From there, there is a for risk that some JavaScript to stop working as expected. This is the case, for instance, of Drupal's misc/teaser.js included on node/add/* pages.
The jQuery update module provides an updated version of jQuery for Drupal. Version 2.x-dev provides jQuery 1.3.2 and a replacement for teaser.js. Shindig-Integrator should depends on jQuery update 2.x or provides its own solution to avoid breaking Drupal's JS.