Continuity mistake: When Michael is talking to Walter, the art dealer, the latter has his hands folded together. In the next shot he has one hand on his lap and the other on the table. (00:35:20)
Continuity mistake: Just after Michael throws his mothers cigarette out of the car, there is a shot from the inside through the front window. There is a large crack in the glass, bottom left of the rear view mirror. When the car is shot from the front, there's no crack. (00:24:30)
Continuity mistake: When Michael drops his mother off at the hospital, she takes her cigarette out of her mouth to talk to him. In the next shot, the cigarette is back in her mouth. (00:26:25)
Chosen answer: They could wear disguises to hide their appearance.