This episode, "The Thirteenth Hat," was the thirteenth episode broadcast.
Commissioner Gordon first refers to The Mad Hatter as "Jervis Tetch", making this the first reference to a super villain's alter ego/secret identity in the series.
Based on a comic book story published in Batman #161.
The Gastonian Institute mentioned by the Mad Hatter is clearly a spoof of The Smithsonian Institute.
After talking to the hat check girl, Batman caught his cape in the door when he closed it. He drives off with the end of his the cape flapping in the door.