Catwoman proposes marriage to Batman, but Batman demurs, saying that a wife would severely impede his crimefighting. In the comics, however, the Golden Age (1930s-50s) Batman did marry his Catwoman, and the marriage produced a daughter, Helena, who grew up to be the Huntress. The Crisis on Infinite Earths, however, wiped all three characters from canon.
A rare event occurred: Catwoman visited the Batcave, being just the third super-villain to successfully do so, after the Joker and Penguin in The Penguin Declines (1967). The Riddler's ill-fated accomplice Molly also visited the Batcave in Smack in the Middle (1966).
When Batman and Catwoman are driving to the Old Criminals' Home, the back-projection behind the Batmobile shows them driving across the Verrazzano-Narrows Bridge in New York; they pass a sign visible above the opposite lanes that instructs drivers to keep left for "Shore Pkwy" and "Eastern L I" (Long Island), indicating that they are driving from the Brooklyn side toward Staten Island. However, Catwoman tells Batman to drive to the Old Criminals' Home on "Short Island" (the Gotham City equivalent to Long Island), suggesting that they might be driving in the wrong direction.
In this episode Catwoman claims she could survive the leap into the river, but Batman reminds her that she wouldn't survive the 200 foot fall down below. This was also the second time that the feline uses one of her "nine lives" (as previously seen in "Better Luck Next Time") when trying to escape the Dynamic Duo. She also claims she can swim; however in the Batman film she panics when Penguin's sub is hit by Batman's blasts and claims that cats don't like water (she and her cat avoided water during the infamous fight scene). In other words, she can't swim!