This is the first episode to feature Keith Taylor as Beaver's classmate Harry Harrison. Perhaps the producers envisioned Harry as a replacement for Beaver's friend Larry Mondello (who was in 67 episodes over four seasons, the last of which was Beaver's Big Contest (1960), three episodes prior to this one) but the character of Harry would appear a total of only eight times in the series, all in season four.
June, whose family background is a mystery except for Aunt Martha and a once mentioned pregnant sister, reveals more. She has a grandfather who was a genius, an uncle that became a judge and she remarked Beaver had a grandfather that was a professor.
The girl behind and to the right of Beaver as the class is taking the test, is writing right-handed in some shots but left-handed in others.