When Serena goes into her tent for the night, her hair is in pigtails. Right after, when she gets into her sleeping bag, it is down, pulled back in a bow.
In the scene where Jim-Bob is riding in the biplane you can see a double tanker on a freeway in the background as the plane lands.
At 38:40, plainly visible in the background as the plane lands, is California Interstate 5, "The Grapevine," complete with a double tanker truck going by. Also in the background on the left side of the screen are modern day electrical towers.
When Jim-Bob is flying and is shown taking the plane into a vertical, the clouds in the background rotate with the plane, showing that the camera was rotated rather than the plane.
At 3:50 into the episode, Godsey's Mercantile is shot from such an angle that it's obvious the dormer on top of the store is just a facade.
Serena decides to go on her hike by herself when John isn't there to go with her, but she had said someone had to witness her do her tasks for her merit badges. It makes no sense for her to go by herself since she won't get credit for it without a witness.