The name Alan is employed multiple times throughout the series for one of Beaver's classmates/friends and the actor assuming the role of Alan changes almost as frequently as the name is used. Here Larry Adare plays Alan. It's his second of two appearances in the series. In his first appearance in Beaver on TV (1963) from earlier in season 6, he plays one of Beaver's peers named Phillip.
In all, Burt Mustin appears in the series 14 times as Gus the Fireman. While he doesn't appear in this episode (he last appeared in Beaver's Fear (1962) from season 5), his character's name is mentioned as Beaver reminisces.
This episode originally aired on 3/28/1963, which is 1,195 days since Aunt Martha's previous appearance in the series in the episode Beaver the Magician (1959), which originally aired on 12/19/1959. That's the longest gap between appearances for any recurring character in the series.
A similar plot was used in Season 1, Episode 35, "Boarding School" (1958), when Wally was considering going to a military academy.