When Ep and Sarah are having a conversation at the memorial, Ep's hair goes from being combed right-to-left to left-to-right from one shot to the next. Update: If you pay attention to the color stripes on Ep's bow tie, it is easy to tell that a reverse image was used for half of the shots.
In one scene it's mentioned that John Walton returned from World War I when his son John-Boy was four years old, and that that was the first time John-Boy had ever seen his father, suggesting that John-Boy was not yet born when his father left. America's active involvement in the war was a little less than a year, so it's impossible that John Walton would have been gone for four years.
At one point, there is a problem with a car having a loose fuel line. Jim-Bob suggests he can fix it since he has a socket wrench with him. In reality, a socket wrench would not be helpful for repairing a fuel line. An open wrench would be more useful.
Grandpa mentions his son Ben wearing his Certificate of Merit Medal when he was home on furlough. During WWI, American soldiers stationed in Europe could not come back to the states for their furloughs as the transatlantic trip would have taken about 14 days and the length of their furloughs were only 10 days at most.
As John-Boy and Olivia drive off to Richmond, one of the walls surrounding the Warner Bros Ranch exterior set is clearly visible.
Jason and Mary Ellen are both less than 4 years younger than John-Boy, so there is no way that John-Boy met his father for the first time at age 4.
Sara asks Sheriff Bridges if he ever got married and he says he did and he has two grown sons. They mention multiple times it's been 19 years since they've seen each other. If he got married right after he came home from the war and his wife got pregnant right away, the oldest his children could be are 18 and 17 (unless they were twins they'd both only be 18 at the oldest.) Not exactly grown and out of the house as implied.
When Jim-Bob talks to Sarah Griffiths at her broken-down car, the boom mic is reflected on the front of the car.