Continuity mistake: In an early scene, the bartender and the bar owner's wife are driving in the rain, at night. The car is a large Ford: at one point, it becomes a mid-sixties Volvo 122, then is shown as a Ford again.
Continuity mistake: In the opening sequence where John Getz and Frances McDormand are driving in the rain, the rain stops and starts, depending on the shot.
Continuity mistake: The wall in the bathroom has a very poor refinishing job. They may have had to practise this shot once earlier.
Continuity mistake: When the PI, Visser, shoots Marty, he is aiming the gun at a somewhat downward angle, then, for just a moment, we watch a surprised Marty stare at him. The camera cuts back to Visser, who is now holding the revolver at a much higher angle, as he contemplates shooting Marty again. The camera pulls back for a long shot and it appears Visser is no longer holding the gun on Marty. In the very next shot, he is again pointing the gun at Marty. Also the blood on Marty's shirt increases substantially in the few seconds before Visser leaves. Without a DVR, these details are very difficult to see (except the gun angle).