After Sol tops off his first tree, he puts his axe on the top. He then climbs up to sit on the top, but the axe has disappeared.
Natty's hat falls off while fighting with Frankie near the beginning of the film. In the next shot, it's back on her head.
When Natty jumps from the water tower to the moving train, she spills water on Harry and the contents of the freight car. Both Harry and the car are dry a few seconds later, when the wolf joins them.
When Natty Gann is escaping the orphanage, she hides in a trunk of a car, which has a spare wheel on the back. In the next scene however, the spare wheel disappears.
The story takes place in 1935, but in the scene where Natty finds the puppy behind the cinema, the movie poster behind her is for "The Buccaneer" (the name of the film star, Fredric March, can be seen in the close up), which was released in 1938.
When Wolf disappears into the woods and Natty has no choice but to run after the speeding train (where Harry is already on board), a camera operator's lower body can be seen sitting on a board that seems to be attached to the side of the train.
The steam locomotives seen in the film have distinctly Canadian vestibule-style cabs.