Continuity mistake: Right at the start of the paintball game, we see that one of the players does not have a hopper (paintball holder) on the top of his marker (paintball gun). And he is firing blanks.
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: Right after the debate, we see Tom Dobbs and Jack Menken walking along the sidewalk talking. From the wide shot we see that they walk past the mail box on the sidewalk. Then when the camera cuts in to the close up, we see then walk past the same mail box again.
Continuity mistake: You can see that Dobbs is wearing a wedding ring in scenes even before the scene of his marriage in the movie.