Alfred claims that Iceland is considering severing diplomatic relations over the kidnapping of Miss Iceland. Severing diplomatic relations is an extremely serious action on the part of a government, one that eliminates all official communication between the party states, closes their embassies and consulates, recalls ambassadors and diplomatic staff, and potentially suspends treaty obligations between the two. No modern state would threaten to sever diplomatic relations over a beauty queen, much less actually do so.
Chief O'Hara describes the day as 98 degrees (Fahrenheit) in the shade, but the stock shot of Batman and Robin arriving at police headquarters has several passersby dressed in heavy overcoats.
As Batman and Robin reach the roof of Mr Freeze's hideaway, in the final leap over the wall, the shadow of Batman's arm can be seen clearly against the sky backdrop.
It seems odd that Commissioner Gordon and Chief O'Hara, both of whom have spoken in person with Batman and Robin countless times, don't pick up on the fact that the imposters' voices are nothing like the Dynamic Duo's.