I have two lists, I want both of them to be sortable and want to be able to copy (drag) items from list1 to list2 and vice versa.
http://jqueryui.com/demos/sortable/
I have to say that FFish's answer to this has been incredibly helpful to me.
I'd make one suggestion; if the lists are being constantly changed the mousedown event seem to be called numerous times because of the re-registering of the event on all the child objects. It might be a bit of a kludge, but I've added an unbind first to ensure the mousedown event is only called once.
$(".album li").mousedown(mStart);
to
$(".album li").unbind('mousedown', mStart).mousedown(mStart);