Uploader's underlying upload manager, SWFUpload has regressed in Firefox 3.5. As a result, it is throwing exceptions on all calls through the Flash bridge after files have been added to the queue.
I've tracked this down to SWFUpload's famous sensitivity about DOM manipulation. It appears that if the Flash browse button is located anywhere near elements in the DOM that are manipulated, or is manipulated itself, the Flash bridge breaks.
The solution to this is to move the Flash browse button outside of the Uploader container into a location where it is isolated.