Plot hole: In the scene in Hess's office, he agrees to save Sophie's son and remove him from the concentration camp. He also tells Sophie that he'll bring her son to see her the next day. In the very next scene, Sophie attempts to steal Hess's daughter's radio which would completely jeopardize the saving of her son if she was caught. It is unlikely that she would jeopardize the wonderful situation she arranged for her son, by stealing a radio. Later, Hess does not save her son, but Sophie didn't know this would happen, so she would not have attempted to steal the radio at that time.
Continuity mistake: When they are having the outdoor picnic celebration, Nathan gives Sophie a dress and a shoebox containing a pair of new shoes. When Sophie puts the shoes on it is obvious that the undersoles are stained and worn.