When Erin picks up Curt's letter, she has glittery silver nail varnish on her nails. This is not visible in any other shots, and does not fit with the time period or with the character, whose parents forbade her from wearing cosmetics.
Mary Ellen's wedding dress was supposed to be Grandma's but it was not the same dress Grandma danced in during the show about her 50th wedding anniversary.
It's not possible that Curt would report Stony Gap mine to the Virginia Bureau of Mines as Stony Gap is in West Virginia.
While setting up for the party, Grandpa gripes, "You'd think the queen of England was coming." Since the episode is set in 1937, it's more likely he would have said "king of England" as George VI was the monarch at that time. This may have been an ad-lib by Will Geer, who was known to improvise dialogue from time to time, and was simply thinking of Queen Elizabeth II.