Cindy Carol, who seconds Wally's nomination for sophomore class president, is making her third of seven appearances in the series; her first of four appearances playing the role of Alma Hanson. She is listed in the credits as Carol Sydes, which is her birth name. She changed her name, at least professionally, when she took on the titular role of Gidget in Gidget Goes to Rome (1963).
In this episode we find out that Tooey's real name is Brian. The teacher calls him Brian during class. (You can clearly hear Brian and the CC says "Yes Brian")
As June and Beaver leave the kitchen after discussing the coconut cake, there is a small teapot on the counter by the door. When Wally comes in and starts to cut the cake, suddenly the teapot is moved over and in its place is a cookie jar which June takes and offers to Wally.
In this episode Ross Elliott plays Mr. Hyatt. In season 4, episode 15, his name is Mr. Foster, Wally's love interest Julie Foster's dad and English teacher to both.
When June offers Wally a cookie, she holds up a Mammy cookie jar, which was a popular kitchen collectible during the 50s.