After stealing the golden calf, the Riddler leaps out of the ballroom window. The actor can be clearly heard landing on the floor outside that window, about three feet below. The next angle shows the Riddler falling from a three-story building with no ledge.
During the fight scene in the flooded bank, Batman and Robin can be seen fighting The Riddler's henchmen underwater. Yet, their capes do not float.
When explaining the pie puzzle at the beginning, Bruce Wayne says that the line he just drew resulted in seven 'slices'. This is impossible as any line bisecting a circle always results in an even number of sections, the result of doubling the number of sections. The first line makes two sections, the second line four sections, and the third line would be six sections and so on.