During the opening recap sequence, the narrator describes Batman and Robin falling through a trap door with the line "is this trip necessary?" This is a reference to the slogan "Is Your Trip Necessary?", meant to discourage travel during World War II to conserve gasoline, and so that rubber and metal that would have gone for replacement parts in cars and bicycles could be used for the war effort instead.
Robin is weighed at 132 pounds, 10 ounces.
Commissioner Gordon breaks the fourth wall briefly after his call to the Bat Cave.
As Batman clings to the wall trying to escape the tiger, narrator William Dozier tells us that "Batman nimbly reverses the polarity on his communicator." "Reverse the polarity" became a well-known catch phrase during this television era, notably on Doctor Who (1963) as Jon Pertwee, who played the Third Doctor, often had difficulty with the "bafflegab" (scientific jargon) the show's writers used.
Bat ear plugs and magnetic climbing bat paws make an appearance here.