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: As Beaver and Wally are starting upstairs after Ward asks them to go change their shirts for supper, the camera cuts from a long shot of Ward across the room in a chair reading a newspaper, wearing a light grey suit, to a medium close-up of Ward wearing a much darker suit, and then back to the light grey.
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: Ward jokes about the boys having two baths in three days, being some kind of record. It then cuts to the boys sitting on the floor in the bathroom, and we can see the hamper at the right with nothing atop it, but when Wally stands up to put CJ back in the "aquarium" the tank lid is lying on the hamper. (00:11:35)
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: 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)
Continuity mistake: Beaver has a frog in hand when Wally is on the phone, then it is not there when Wally hangs up the phone. (00:10:35)
Continuity mistake: When Beaver goes to Penny's front door, the door changes in appearance from one shot to the next. (00:23:05)
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: As the boys are playing basketball at the Cleavers' house, Tooey is shown in the first shot without his glasses, but immediately in the next shot where he shoots for a basket, he is wearing them. Magical glasses, indeed.
Continuity mistake: June makes Ward go to school to talk to Mrs. Rayburn. She says Mrs. Rayburn was her teacher and still makes her nervous. In Beaver gets 'Spelled episode, June doesn't recognize the name of Mrs. Rayburn on the flowers. Ward says that the only Mrs. Rayburn he can think of is the principal at school.
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: In the scene where Ward is waiting for the boys outside the movie theater, several kids are seen walking out of the theater more than once. A brunette girl in a plaid dress is seen walking out at least six times. (00:02:00)
Continuity mistake: While Wally, Beaver, and Eddie are talking about military school, Beaver is sitting inside a car tire swing, and depending on the shot, the tire's whitewall stripe either faces away from Beaver's front or his back. (00:17:25)
Continuity mistake: When Linda is up in the tree talking with Beaver, her hair braids keep changing position; sometimes they're over her shoulders and sometimes not. (00:05:00)
Continuity mistake: In the scene where Ward helps June carry the groceries into the house, the bag in his left arm has a loaf of bread sticking out of the top, but as they enter the kitchen the bread is sticking out of the bag in his right arm. It is not even the same size.
School Play - S2-E11
Continuity mistake: After the school festival performance, when Beaver reveals himself as the mushroom, the two costume straps hang straight down over Beaver's shoulders, but in the wide shot the two straps are crisscrossed, then reverts back to the original way. (00:22:20)
Continuity mistake: While Beaver and Larry are watching the "corkscrew" digging a hole, when their books and lunchboxes are run over by a truck, the damage changes in the following shots. (00:04:40)
Continuity mistake: When June enters the boys' bedroom at nearly 1:00 am, she turns on their light. In the closeup, she flips the light switch, which is already in the up position, and the light turns on, but in the next shot, the light switch is in the down position. Then, when June exits their bedroom, in the wide shot, the light switch is in the down position, but in the closeup, the switch is in the up position so she can flip it down (off). (00:06:35)
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)
