When Batman and Robin are climbing the side of a building, Colonel Klink from Hogan's Heroes (1965) pops his head out of a window and talks to the Dynamic Duo. It's not only odd to have the heroes of this show talking to a character from a different time period, but this was one of the first times a taboo had been broken, namely using a guest from a show on a rival network (Batman was shown on ABC TV and Hogan's Heroes on CBS TV). Batman even says, "Be sure to say hello to Colonel Hogan from us."
This episode, in which Robin is shot by the criminal cowboy Shame, was rumored at the time to have been a "silent" protest against the Vietnam War; it was said to have been subtly drawing attention to the fact that soldiers almost as young as Robin were being shot and killed every day. (Only Robin wasn't killed, of course!)
Laughing Leo, the used car salesman is standing next to a fancy hot-rod telling an old lady in it what a great deal she made, and she says she certainly hoped so, since she drove all the way down from Pasadena. This is a nod to the popular Jan & Dean song "The Little Old Lady from Pasadena", which featured a sweet old granny from Pasadena whom had a red Super Stock Dodge parked in her garage; she drove fast, hard, and was a terror, and indeed, as the old lady pulls out of Laughing Leo's, she guns it. The song was a hit two years before the show came on the air. (The song was recorded by Jan & Dean in March, 1964, then performed by The Beach Boys in August, 1964 for their LIVE Album.)
This show was famous for its use of stunt casting and inside jokes, some of which are probably lost on people now. One of them is found in this episode, a parody of Shane. At the time this was originally broadcast, ABC also had a TV version of the movie, with Christopher Shea playing the role of Joey Starett. In this Batman, there is a little boy who rather closely mimics Joey Starett in the movie. As it turns out Eric Shea, who plays the little boy, is the younger brother of Christopher Shea, who played Joey in the TV version, which was on the air at the same time, although its last episode was broadcast a couple of weeks after this Batman episode.
Comedian Jack Carter makes another uncredited appearance as musical maestro DJ Hot Rod Harry.