Visible crew/equipment: After Eddie tells Wally that it once took his father two days to make a breadboard, when it cuts to Beaver walking into the kitchen, the curved chalk actor's mark is visible on the floor where Beaver stops. (00:09:35)
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)
Visible crew/equipment: When Wally and Beaver go downstairs to tell their parents about being at court earlier, Wally stops at the edge of the rug and his curved chalk mark is visible on the bare floor. (00:22:15)
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)
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: 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)