When Mario and Luigi are under attack after they wake up and the house goes underwater, the hammer brother that chases around for Mario and Luigi frequently changes colors.
When Koopa is chasing Mario and Luigi with his doom sub in Venice, Mario's hat disappears and reappears in different shots.
The windows on the 'Doom Sub' change shape and placement between shots.
(at about 3 minutes 45 seconds) As Mario and Luigi row away from the shot, the edges of the two translucent layers of animation cels can be seen panning to the left as well, causing the picture's brightness to increase.