In the opening scene in the classroom, there are two sentences on the blackboard: "Albany is the capital of New York" and "Sacramento is the capital of California". Several days later, in the final classroom scene, Miss Canfield is shown erasing the blackboard. The two sentences about state capitals remain.
As Ward reads the note that came with the roses, he says, "Hope to see you back on your feet soon." When June reads it a moment later, she says, "Hope to see you back on your feet again."
When Wally types "Theodore" on the note to the teacher, he types only seven letters, not eight.
When Wally is typing the note for the teacher, he initially types "Beaver", then Beaver corrects him, saying they call him "Theodore". Wally then types a series of "XXXXX"s over the word "Beaver" and then presumably types "Theodore". But there is no space for him to type "Theordore", since it is immediately followed by the next sentence ("I have whipped him").
Stanley Fafara played Beaver's classmate, Hubert 'Whitey' Whitney, in many subsequent episodes. In this early episode (the first one broadcast), when Miss Canfield speaks to him in class, she calls him "Harold".