Actually, if you watch REALLY close (1" from the screen would be good... (pause it, and
then go frame by frame), you'll see that the cat actually goes length-wise the moment
before Duke gets up. Since the scene is shot at an angle, we don't get to see a portion
of the stairway. When you pause-advance the frame, you'll see the cat's tail go diagonally
down the steps. It's more of a poor camera shot than a slip-up.
Oh, BTW, the Japanese sailors' name is Matsuo, not Motsu. Motsu is a verb. :) (to hold)