Continuity mistake: In season 1 (1957), Beaver is in grade 2 and Wally is 13 and in grade 8. Tony Dow was born in April 1945 and Jerry Mathers in June 1948. This means that Beaver/Jerry would have been 9 and Wally/Tony Dow 12, with a 3-year age gap. In the last (6th) season, Wally is a senior which indicates that he must have failed a grade. Meanwhile, Beaver is in 8th grade. Interestingly, the actors were also 3 years apart in age. At age 12 in 1957, Wally should have been in 6th/7th grade, which is more consistent with him being a senior in season 6.
Continuity mistake: After Ward puts a new lightbulb in the fridge June stares at the mess Ward made, and the scalloped range hood vent is conspicuously missing, but when Beaver walks into the kitchen, the hood vent is back in its proper place. (00:17:10)
Continuity mistake: During the dinner scene, in the wide shots of the family there's a mirror hanging on the wall above the sideboard behind June, but in the shots facing June the mirror is gone. (00:02:15)
Captain Jack - S1-E3
Continuity mistake: When Wally and Beaver are caring for the baby alligator in the bathroom, Beaver holds out his left index finger and it gets nipped by Captain Jack, but next shot Beaver's holding his injured right index finger. (00:11:30)
Captain Jack - S1-E3
Continuity mistake: Where's the puppy that the boys get at the end of this episode throughout the rest of the series?
Suggested correction: In episode 1x23, Beaver and Poncho, when Beaver brings home a lost little Chihuahua, he shows his parents and asks to keep him. Then Ward tells him, "You and Wally had a dog once, remember? You didn't take care of him. We had to give him away." This explains what happened to the dog from season 1, Captain Jack episode.
Continuity mistake: At the start Ward drives up in their old 1959 Plymouth Belvedere. He had been driving the 1961 Plymouth Fury for some time in season 4.
Continuity mistake: In "The Credit Card" four episodes before this one, Eddie uses the $15.00 that Wally pays him from a loan to buy a vest. Later Eddie has to give the vest to a friend in order to get back money owed to Eddie's father. But in this episode we see Eddie at Lumpy's party wearing the very same vest.
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)
Continuity mistake: When Beaver walks over to the window to look outside, the window is fogged up due to a rainstorm. But when he gets there, the pane of glass he looks through is clear - without his having had time to wipe it off. (00:03:05)
Continuity mistake: When Beaver and Wally are examining Ward's old trunk, two of the pictures of June taped to the inside of the lid go from being a couple of inches apart to right next to each other to apart again. (00:07:05)