The yellow rose bouquet changes from full bloom to closed buds and back again between scenes.
At 35:35 Grandma says she raised three children in the house. Subsequently it's established that Grandma and Grandpa only had two children, John and his brother Ben who died in WWI. The mysterious third child is never mentioned again.
Correction: Grandma says she bore three children, not raised. In the Season 1 episode The Typewriter, Grandpa shows John-Boy a picture of Amy, a child who died of Scarlet Fever in childhood. Though it's not specified, this is probably the third child Grandma is referencing.
At around 1:50, when Olivia leans out the window to call the kids in for dinner, it's obvious that they're on a soundstage as her voice echos and reverberates, which it would not do if she was shouting outside in the open air.
The voice actor reading FDR's radio speech sounds nothing like FDR.
In the ending narration, John-Boy says that later in life Mary Ellen was married to a professor, lived in Richmond, and had two children. These details are not in agreement with what did in fact happen to Mary Ellen in later seasons of the series and in the post-series holiday special movies.
John Boy's ending narration mentions that Mary Ellen later married a professor, had two sons, and lived in Richmond. However, in Season 5, Mary Ellen ends up marrying Dr. Curtis Willard, and they later have a son Joh Curtis. Curtis is killed off killed off in Season 7. In Season 9, she marries a character named Jonesy.