Corrected entry: At the end, Batman mentions "Aunt Harriet's home-cooked meals" to Robin while they're well within earshot of Riddler and his henchmen, who are all restrained, but not unconscious. That's dropping a pretty big clue to their secret identities - a mistake Batman would be much too smart to make. (00:22:00)
The Penguin Declines (3) - S2-E39
Corrected entry: After all the stow-away baddies jump from the Batmobile's trunk, they leave it open. Between shots, it magically closes itself. (00:19:30)
Correction: When the baddies climb out from the Batmobile's trunk, the trunk is open at 00:17:43. Then we don't even see the trunk again until 00:19:54, when the brawl breaks out, and Robin jumps atop the Batmobile and slams the trunk closed.
The Joker's Provokers (2) - S2-E22
Corrected entry: While Batman and Robin are going over clues, one of them is O-HO. Robin says it's the formula for water, which is H2O. The two is attached to the H, not the O. O-HO should have led to hydroperoxyl, which is HO2.
Correction: Mentioning Aunt Harriet's name would hardly be a clue to Batman's secret identity. First, she isn't even Batman/Bruce Wayne's aunt. Additionally, other non-relatives (like the Commissioner) call her Aunt Harriet. And, even though the audience can hear Batman, there's no reason to think the goons are in "ear-shot".
Bishop73