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.
Other mistake: During almost any random episode of the family hanging out on the porch after dark, the moonlight is unusually bright, indicating obvious studio lights in their faces, or plug-in lamps on extension cords for actual light attached to the porch ceiling or whatnot.
Factual error: Considering it is the Depression, it is highly unlikely that the family would have any electricity in The House. With maybe the exception of a lamp or two, as rural folk typically didn't have such accommodations in 1930. Yet every room has some form of fancy lighting display.
Other mistake: Maryellen wears visible eyeliner throughout the show, despite being during the depression. She wouldn't be wearing any makeup.
Suggested correction: Why wouldn't she be wearing makeup during the depression? Especially if it was just a small amount. This isn't a mistake, just your opinion. Women continued to wear makeup during the depression, and not just starlets or the rich and famous. In fact, makeup sales overall hardly took a dip during the depression because women through the US were still buying it.
Despite that women did wear it during the Depression, part of the factor being that the Waltons wouldn't afford such a luxury, considering their very tight pockets. Otherwise, we'd see Olivia preening herself also, before she goes anywhere. But doesn't even wear lipstick. And Maryellen is never 'caught' actually putting on the eye makeup. So it's likely not any opinion.
Continuity mistake: All of the children, even John and Olivia, seem to have reddish/auburn hair. Their natural hair colors are used in later seasons.
The Homecoming: A Christmas Story - S1-E1
Visible crew/equipment: When Olivia calls for John-Boy he jumps from his bed and hides his journal, then as he heads to the door the shadow of the boom mic dips way down into view. (00:27:25)
The Homecoming: A Christmas Story - S1-E1
Visible crew/equipment: While John-Boy is upstairs writing in his journal about growing taller, when it cuts to Esther and Zeb downstairs, the shadow of the moving boom mic is visible just as Olivia wonders about John-Boy's whereabouts. (00:48:35)
Visible crew/equipment: When Ep comes to take Holly away John changes his mind, and when he invites Ep for coffee we can see the T-mark (plastic type) on the ground, where Esther and Zeb will stand in a moment. (00:14:45)
Continuity mistake: After Elizabeth tells her mother that nobody cares about her, while she sulks on the porch there's a wideshot of the girls playing catch with Holly, then as the camera is dollying out Holly's mother comes into view at the left and she's wearing a sweater, but in the next closeup the sweater has vanished. (00:32:40)
The Carnival - S1-E3
Continuity mistake: When Esther breaks her eyeglasses, in the closeup as John-Boy picks it up half of its right lens is gone, but in the wideshot as he hands the glasses to Olivia that lens is still intact. (00:03:20)
The Carnival - S1-E3
Factual error: After John-Boy reads the scary bedtime story to Jim-Bob and Elizabeth, when Elizabeth is lying in bed she's holding her Raggedy Ann doll, and in the closeup we can see the doll's Knickerbocker tag. This episode takes place in 1933 (the Chicago World's Fair is mentioned at the end), and the Knickerbocker Toy Company created this doll in the late 1960s. (00:09:30)
The Carnival - S1-E3
Continuity mistake: While John and Zeb are making the train arrangements with Sam, just as Zeb calls Homer an old priss Sam opens the clock dial's top hinged glass door in the wideshot, but in his next closeup that door is suddenly shut and it's the pendulum's bottom glass door which is now wide open. (00:29:55)
The Carnival - S1-E3
Revealing mistake: When Jonboy, Jason, Ben, and Elizabeth are trying to lure the monkey down from the tree, the leash it's tethered to is visible down the tree trunk. But then disappears after the monkey climbs down.
The Carnival - S1-E3
Visible crew/equipment: Near the end, when the clowns are performing their act for the Waltons, the monkey's leash is visible as it makes it way across the tightrope, before jumping down.
Visible crew/equipment: After Miss Hunter tells the class that the spell down between the finalists will continue the next day, when it cuts to the long shot of the kids coming home, we can see the crew's production truck at the top, right side of the screen. (00:17:35)
Visible crew/equipment: After the Colonel tastes the Recipe and asks about it, when Polonius tells his friend that the "secret" is the Recipe machine, the shadow of the moving boom mic is visible over Polonius. (00:31:10)
The Sinner - S1-E8
Visible crew/equipment: At the start, while Miss Prissom and Matthew Fordwick are driving to the Waltons they are alone in the vehicle, but when Miss Prissom tells Matthew about the Buddhists from her village, we can see the hand of a crew member moving around behind Miss Prissom. (00:02:25)
The Sinner - S1-E8
Continuity mistake: After Zeb and Matthew's visit to the Baldwin sisters, when the singing duo arrive at Godsey's store while everyone is watching, the man driving is wearing a different shirt than Zeb and is considerably younger. (00:35:05)
Visible crew/equipment: After Jason tells John that he left word with Ike for the Sheriff, Elizabeth runs into the barn worried about Pete. Then Gino walks over to his T-mark (plastic type) on the dirt ground and a second T-mark (partially covered in dirt) is beside it. Soon, John-Boy walks over to that second T-mark as he glances down to presumably be certain he hits his mark. (00:32:55)
Visible crew/equipment: When the Charlottesville taxi parks in front of Godsey's store the taxi door opens, and the reflection of a crew member is visible on the door's window. (00:02:40)