The last sentence of The Riddler's typed riddle reads, "And of every race." When Robin reads it back to Batman in the Batcave, he reads it as "and the end of every race". The typed message omits the words "the end".
When preparing to climb the building they are at the left side of the building plane. When actually climbing they are on the right side of the building. This climbing scene has been used in many other Batman episodes.
Batman and Robin don't solve The Riddler's riddle: "What is the beginning of eternity, the end of time and space, the beginning of every end, and the end of every race?" In the following episode, it's shown on a blackboard in the Bat Cave in a list of riddles. There's a check mark next to it indicating they solved it, but they never solved it on camera nor explained its relevance. (The answer, by the way, is the letter E.)