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: 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: 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)
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)
Visible crew/equipment: When Ward tells June he wants to take the boys to Friends Lake, for an overnight camping and fishing trip, as Ward heads for the staircase so he could tell the boys, he passes a piece of filming equipment which is visible at the right side of the screen. (00:08:25)
Visible crew/equipment: When Mrs. Bennett shows up the second time and tells June that she'd like to give Beaver a reward, the curved chalk actor's mark is visible on the floor near the staircase, and it's where June will stand after Poncho and his "mother" leave the house. (00:21:05)