Visible crew/equipment: The shadow of the boom mike is visible in the background when Wally is saying that June looks "ritzy". (00:14:45)
Teacher Comes to Dinner - S3-E9
Continuity mistake: As the family is sitting at the breakfast table during one of the very first scenes, Beaver gets up to leave for school. The checkered napkin in his lap falls to the floor as he walks to the back door. The camera cuts back to the table where the napkin has magically reappeared.
Continuity mistake: When Ward is talking to Beaver in the bedroom, he stands behind Beaver and is in the process of combing his hair. When Ward sits on the dresser, Beaver's hair has somehow finished being combed. (00:24:18)
Visible crew/equipment: Beaver is pretending to have a football game with himself. You can see the boom mic shadow to the left of him and it continues all the way to when Wally and Beaver go sit on the bench. (00:10:45 - 00:11:11)
Character mistake: As Eddie Haskell and Lumpy Rutherford return from the washroom to Mr. Gannon's history class, Mr. Gannon calls Eddie "Louis."
Character mistake: When Gilbert and Beaver are talking to their English teacher in the classroom, the teacher addresses them as Mr. Cleaver and Mr. Harris (as opposed to Mr. Bates). This same name discrepancy is referenced on this site in another episode.
Continuity mistake: There are a couple of continuity errors in the dance scene: First, the 4 girls sitting across from the boys switch positions from one shot to the next, then the last girl (long dark hair) disappears from the row of girls entirely, only to show up on the dance floor later in the scene. She was across from (and should have been paired up with) Beaver; instead, the teacher nods toward a now-empty chair and remarks that they "ran out of girls". (00:08:00)