Marta Kristen (Jiffy Snack Girl) would later go on to co-star with Bill Mumy (Jackie Chester) in Lost in Space (1965).
The house used is the same one as on Leave It to Beaver (1957) as both were filmed on the Revue / Universal set.
This was one of 17 episodes directed by Alfred Hitchcock himself. Bill Mumy, who was about age 7 when the episode was filmed, related in an interview that he had trouble hitting his mark so that he stayed within the key lighting on the set. According to Mumy, Hitchcock became so frustrated that he took Mumy aside and quietly said words to the effect of, "If you can't stay in your proper place on the set, we'll get a nail and put it through your foot, and blood will come pouring out like milk."
Bill Mumy would go on to portray another young boy who finds a gun in the Perry Mason episode The Case of the Shifty Shoebox (1963). Coincidentally, that episode was also the second episode of season 7.