Drag the TabPane or the WebPane from the Library, move the mouse into the content panel, move out and move in, you will see the exception.

The problem is that
1) PrefSizedTransferable.getData() will return same data, but its parent (or all other Transferable object) will create a new one everytime the getData() is called.
2) EditModeController checks to have a new data everytime when it calls getData() (Line 578)

I think it is better to remove that check in the EditModeController (perhaps we can check that the element of the data is not added to any element container), and make all Transferable return same data.