Continuity mistake: While the unconscious Robin is being carried away from the Batmobile by one of Riddler's thugs, his cape loosens and appears to completely fall off just before they exit the frame. In the next shot, Robin is still being carried away but his cape is securely back in place.
Factual error: A fictional country is shown in this episode, with the name "Republic of Moldavia." It is portrayed as a south-eastern Asian country (the exterior shot shown was from the Thailand exhibition at the 1964 New York World Fair), but it's quite an odd choice to use as fictional name a name of a principality that historically did exist, in a completely different part of the world, where the current Moldova is.
Continuity mistake: In the cliffhanger, Riddler is putting a vice around Robin's head and cranks it; in the close-ups he turns the mechanism between his fingers, while in the shot from behind Robin's head he is turning a little handle. The height the vice is placed at is also different. (00:24:20)
Continuity mistake: The Moldavian host calls attention on the national treasure before the cake is brought. In the wide shot, just before the cut you can spot the man in white uniform turning his head to his right. In the next shot he is turning towards his left. (00:01:05)