Stupidity: Batman and Robin tore apart the umbrella looking for clues to the point of micro-analyzing the fabric and the ribs, but they did not look at all into the largest and most obvious hiding spot; the handle.
Stupidity: Whatever Batman thought he was throwing instead of the confetti bomb from the belt the Joker switched with his own, the Joker had already long left - why would he throw anything at all, in an empty room?(00:12:35)
Stupidity: The conveyor belt has two different flip switches; one saying START, the other STOP. Who would ever design that, when an on/off switch is more than enough?(00:23:50)