Deliberate mistake: When Mary gets to the school where she is going to be teaching, all the children are standing outside wearing shoes. However when they come in to the school they are barefoot. I have a feeling this was done to show how poor the community she was teaching in was supposed to be, but it looked like too cold and rainy of a day to let the actors be outside barefoot.
Tall Woman in Red Wagon - S1-E6
Deliberate mistake: When the workers hit the coffin lid with the shovel, it is (obviously) fully buried and they moved just a little bit of soil off it. Rockford moves closer, and instantly the inside of the coffin is covered by the thinnest layer of dust, uniformly. (00:02:30)