Continuity: When the Hawks are chasing Professor Brainard and Betsy, the two policemen are shown approaching the area in their squad car, a 1956 Ford. However, when they arrive on the scene, they are driving a 1960 Ford.
Continuity: When Alonzo Hawk is talking to Ned and Betsy about 'merging together', Betsy is putting on his flubberized shoes. Right before Alonzo gets up you clearly see that the soles of the shoes do not have Flubber applied, although he jumps as if he did. He never changes shoes.