Deliberate mistake: There is a huge security breach in the scene with Robin Williams and Christopher Walkin walking at night. The Security SUV limousine is more than 30 metres away from them. It should be pacing them in case of an emergency and be right next to them on the sidewalk. It appears the reason it is so far back is because at the camera angle the scene is shot at, it makes for a good background element which you would not see if the Secret Service followed protocol.
Continuity mistake: In the scene where Laura Linney is talking to Christopher Walken at the Thanksgiving party, he is sitting in his chair smoking a cigarette next to a patio door. During their conversation, while the camera is facing Christopher Walken, he is holding his cigarette in his right hand. When the camera changes to face Laura Linney, his cigarette is visible over his left shoulder and is held by his left hand. When the shot changes back to face him, it's back in his right hand. The shots seem to move too quickly for him to have switched hands between them.
Continuity mistake: You can see that Dobbs is wearing a wedding ring in scenes even before the scene of his marriage in the movie.