[The question is somewhat obsolete; the new behavior does something reasonable on a paste when you've copied an entire row. As far as I can tell, there's still no way to move a row directly. The workflow now is copy a row, insert a new blank row where you want one, paste (the paste now inserts the row correctly), and delete the original row.]
How do you move rows in a Document table? The obvious thing - selecting the entire row, cut, paste - does something very strange (inserts the row as a single cell with a nested table containing the cut row).