Deliberate mistake: In the opening of seasons 2 onwards, there is a photo of Olivia outside the Church with the family. This is a scene from Season 1 Easter Story. However, it had to be from an outtake because the position of Erin, the absence of Jason, is different than what is shown in the episode. It's just something I noticed when I identified from where the shot was taken.
The Waltons (1972)
1 deliberate mistake in show generally - chronological order
Starring: Eric Scott, Jon Walmsley, Judy Norton, Mary Beth McDonough
Visible crew/equipment: At the mill, when John tells Buck that Willie Brimmer might be at the Montgomery cabin with Jim-Bob, in the next closeup of John we see a billowy trail of cigarette smoke at the bottom right corner of the screen, but the only people standing there are Elizabeth, John, and Buck, and none are smoking. Presumably, it was someone offscreen smoking too close to the camera (similar to a mistake in 1978's "Halloween"). (00:26:05)
The Reunion - S1-E14
Ike: How's it feel to be a working man?
John-Boy: Ike, Mama would skin me alive! Everyone knows those two ladies make bootleg whiskey.
Ike: But they don't know what they're doing. They're just following their papa's Recipe.
John-Boy: But sometimes they sell it!
Ike: Yeah, but they're just like two little girls by a roadside selling lemonade.
The Journey - S2-E1
Trivia: While Maggie MacKenzie and John-Boy are at the Mermaid Restaurant, when they both dance together Maggie envisions her long deceased husband, Michael MacKenzie, dancing with her instead of John-Boy. It is Earl Hamner Jr. who portrays Michael MacKenzie in this uncredited onscreen cameo during the scene (note teeth and facial features are identical).