John-Boy's mention of ESP experiments at Duke University are based in fact. Dr. JB Rhine conducted these experiments at Duke in the early 1930s leading to the publication of his book "Extrasensory Perception" in 1934. His findings were largely discredited.
The mutton tallow poultices discussed by Zack and Horace were common Appalachian folk remedies of the day. They could include a mixture of mutton tallow (rendered mutton fat), kerosene, turpentine, lard, camphor, pine tar and soot. They were often foul-smelling which is probably why Horace chooses to "keep the pleurisy."
On the way to the train station, John veers his truck off the road because he thought he saw something in the road. If you carefully watch the part right before the accident, you can indeed see a dark blur dart in front of the truck.
Olivia mentions that Luke's mother died in the "...influenza epidemic five years ago," referring to the 1928-29 flu epidemic, one of several that followed in the wake of the disastrous 1918 Spanish flu pandemic.