In the kidnap scene, when Skip Parker leaves Barbra Gordon and arrives at the Hang Five he is barefoot. Yet when the Joker and his crew are carrying Skip Parker from the Hang Five to Joker's car, he is wear a pair of white sneakers (plimsolls) and is no longer barefoot. The sneakers look to be white canvas slip-on and he's not wearing socks.
In the scene were the villians are running from Batman and Robin, Joker's henchman were barefoot but when they ran into the building, they suddenly had shoes on and socks could be clearly seen also.
During the surfing challenge, Batman is threatened by a shark. To counter it, he makes use of Shark Repellent Batspray--something which was first employed in the 1966 movie.
The surfing footage used in this segment was borrowed from the 1966 Cinema V film The Endless Summer.
The Jokemobile appears for the second and last time on Batman in this episode.