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)
Revealing mistake: The purple dress that Micky and Davy bring for Mrs. Weefers to wear is too big for her, showing that the dress was made specifically for Micky to wear.
Revealing mistake: When Cissy is at the piano as Buffy sings and dances for Uncle Bill, only her arms move up and down instead of across the keys, indicating that's it's an off-camera person actually playing the tune. (00:16:30)