Deliberate mistake: Although it was done for plot purposes, no school photographer would only take just one shot of a class photo. They generally take up to 15 to 20, as it is difficult to get everyone to look at the camera and smile at once (and hopefully not pull silly faces).
Leave It To Beaver (1957)
1 deliberate mistake in season 4 - chronological order
Starring: Barbara Billingsley, Hugh Beaumont, Jerry Mathers, Tony Dow
Other mistake: The opening credits for season 5 show June coming out of the front door with a pitcher of what looks like iced tea, and calling for Ward, Wally and Beaver who are all working outside. But the door opens by itself as she comes out, and then closes by itself behind her. If the entire family is outside, who opened and closed the door?
Theodore "Beaver" Cleaver: You know something, Wally? I'd rather do nothin' with you than somethin' with anybody else.
Captain Jack - S1-E3
Trivia: The episode "Captain Jack" was the first time a toilet was shown on TV; the boys buy a baby alligator and Wally is shown putting it in the toilet tank. The network censors were so spooked by the thought of showing a toilet on television that they delayed the episode. And when the censors finally relented, the compromise allowed only the toilet tank to be shown, not the bowl.