Why would they use the same actress as the newspaper delivery girl and the locket girl? In the same season, doesn't make much sense. Must have been a shortage of talent in 1962.

The should have had the actress that played Myra play the paper girl.

I don't profess to know that much about casting, but there are many examples in series of an actor playing different roles in episodes quite close together. In LITB, besides this girl, there is Wendell Holmes, who plays a teacher at Beaver's school and also Andy the alcoholic. And doesn't Pamela Baird [Mary Ellen Rogers] also play Myra, the girl whose mother thinks she should wear an orchid to the dance? And, of course, there are cases in which a new character is played by someone who recently played a one-timer, such as Cheryl Holdridge, who first played Gloria Cusek, then had several appearances as Julie Foster.

Perhaps there are agreements, pushed for by agents, that specify the actor is to have more than one appearance before a contract will be signed, or a one-time appearance is sometimes just an audition, per se, for a recurring role.

Jack Webb, of course, took this to a different level, using the same actors for Dragnet or his other series a dozen times a season. His "stock company," it was called.