Smack in the Middle (2) - S1-E2
Revealing mistake: While Riddler is with the unconscious guests at the Moldavian exhibit, in the basement of the Moldavian Pavilion the Mole Hill gang blow up the ceiling to create an entry to the exhibit, on the floor above. They lean two tall ladders at the side of the hole and climb up. When Riddler makes for an escape Batman follows him down below, and now we can see long metal brackets bolting the ladders to the floor for safety. (00:20:20 - 00:22:00)
The Day Nothing Happened - S2-E20
Revealing mistake: The snowman is an obvious Styrofoam props the kids have set up in the family room, as the fake snowflakes fly right off it during the kids play, including the white patches beneath the body.