TypeError: Error #1009: Cannot access a property or method of a null object reference

[5TonsOfFlax]

Your target determination code is really weird. Since these DragDrops have a _targetPiece property already set, you should use that rather than composing a name and then getting a child by name. Since the targets are not children of the DragDrops, the getChildByName will return null, and it'll never match.

private function dropMovie(event:MouseEvent):void{
  this.stopDrag();
  this.filters = [];
  stopDrag();
  if (dropTarget != null && _targetPiece.contains(dropTarget)){
    removeEventListener(MouseEvent.MOUSE_DOWN, dragMovie);
    removeEventListener(MouseEvent.MOUSE_UP, dropMovie);
    buttonMode = false;
    x = _targetPiece.x;
    y = _targetPiece.y;
  } else {
    x = _origX;
    y = _origY;
  }
} 

Also, you should change the type of _targetPiece from * to DisplayObject.