It's a well-known issue that you can't multi-select in AdvancedDataGrid in Firefox, if you have wmode=transparent.
This site: http://www.johanvanmol.org/content/view/47/41/ gives a nice general work-around for Flash, but after spending hours wading through the AdvancedDataGrid code, I haven't been able to figure out an easy work-around specific to that class. Has anyone else written one? I've narrowed it down to AdvancedListBase::mouseDownHandler, which calls selectItem() with bad values for event.shiftKey and event.ctrlKey. I could just override selectItem(), but it's called in other places that deliberately pass in null, so it would be hard to avoid breaking deselect.

