Revealing mistake: Throughout most of the episode, The Car is a standard black with chrome trimming. But at the end it's suddenly beige when Johnboy and the kids are polishing it for their first ride.
Suggested correction: At the end it's not "suddenly beige." Mid-episode Mary Ellen mentions a family project to, "Design you a new-looking car" and Erin adds, "We can paint it." Soon John-Boy says, "I'd like to paint it a nice dignified shade of tan." In the penultimate scene John-Boy drives Hyder and Martha Rudge back home. Time passes offscreen. It cuts to the final scene with Mary Ellen and Erin placing their new cut/sewn seat covers in the newly painted tan car, and nobody is "polishing it for their first ride."
Other mistake: When Elizabeth's horse takes the bad fall, Maryellen tells them it has a broken hoof. So they put the horse down instead of taking it to a nearby vet for help.
Suggested correction: This episode takes place in 1945. We see Mary Ellen look toward the mare's front (not hind) legs/joints, which are weight bearing; and when Mary Ellen tells Elizabeth about her mare, Molly, Mary Ellen's actual words are, "Elizabeth, it's her leg. It's broken. It's bad. We're gonna have to put her out of her misery." Viewers are not shown what Molly's "bad" break is, but with Mary Ellen's words, we know the break is severe, which was a death sentence for any horse. Just to add, it all completely depends on the location of the equine injury and the severity of the break/fracture. Nowadays, with modern advancements in equine veterinary care, (thankfully!) some severe breaks may not be a death sentence for a horse.
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.