When Robert Foster is talking to the Man in the Yellow Suit at the police station, the right-hand side of the collar of the man's shirt keeps on going up and down between shots.
When the Tucks are in jail and Winnie and the boys are going to help them escape, it shows Winnie crossing the street with all the wind blowing the dust around but the rope at the gallows is hanging still.
Incorrectly regarded as an anachronism:
When Joshua Jackson and Alexis Bledel's characters go swimming she tells him that she cant swim and he says "you're joshing me" which was a popular saying in 2002, but was not in existence in the time period (early 1900's) when the scene takes place.
The word "joshing" in this usage originated in the mid-1800s, and began to surge in popularity at the turn of the century. It was a perfectly reasonable word for that time period if Jesse liked using the latest slang.
When May is walking around in her jail cell playing her music box, the sound of her foot steps do not match up to the speed she is walking at.
After hundreds of years, All they could think of is kidnapping anyone who comes across the spring and considers drinking from it? It would have been a much easier choice to just board up the area around the spring.