I confirmed the behavior by temporarily installing the theme into another of my WordPress 2.8.6 sites, as well as my WordPress 2.9 Beta 2 test site. In all three cases, the Dewdrop theme kills the AJAX features in the dashboard. On the 2.8b2 dev site, I also tried deactivating ALL plugins, isolating the theme as the root problem.
The first question that comes to mind is "what version of Carrington is this based on, and how simple would it be to upgrade the core files to 2.2?" I was under the impression that the main purpose of using a "theme framework" was that the underlying framework could be easily updated without affecting the customized theme. I don't see anything in this theme's PHP files that jump out at me as identifying the version of the underlying Carrington framework.