During Robin's ordeal on the rack, the point at which his wrists are tied to the framework keeps changing: in some shots, his arms are extended above his head; in others, they're bent at the elbows.
When Robin scales the outside wall of the Gotham Museum, Batman has two large yellow boxes on his utility belt. In the next shot of Batman, they are gone.
Batman analyzes the Riddler's wax, and mentions to Robin that it contains nitrogen, uranium and sodium-symbols "N", "U" and "S". "S" is the symbol for sulfur; "Na" is the symbol for sodium (Latin "natrium").
The still shot of the wax Riddle is reversed. The curl of the question mark below his neck is backward.
There is a jump cut in the opening. After the director credit, Batnan's right ankle turns out and forward. Then suddenly both legs are bent out together.
The thin body wires holding up Batman and Robin to the winch are visible.
Batman mentions Aunt Harriet to Robin while The Riddler and his goons, especially Moth, are in earshot.
In the museum, the Riddler incorrectly describes a pillory as the stocks.