A while back I started a discussion in the jQuery Accessibility group: Screen-readers and UI modal dialog. I was really happy with the quality of the discussion that my question generated, and thought I'd take a moment to share some of my thoughts and conclusions. I want to be clear that the ideas that I am sharing here were only made possible through the people who were so willing to collaborate with me in this discussion.
Dragging and dropping or re-ordering objects is a challenge for screen-reader users on pretty much any platform, especially on the web. There are some solutions, like the Fluid Infusion Image Reorderer widget, which uses WAI-ARIA to create an accessible experience for users of assistive technologies that support WAI-ARIA. Drupal implements a complex UI component called "table drag".