During a meeting of the "MOD" squad, Polly Bailey mentions her upcoming appearance on Dateline NBC. Bobby Jay Bliss asks if Diane Sawyer or Sam Donaldson will do the interview, and Polly replies "Sawyer." None of this makes much sense because both of those reporters work for ABC not NBC.
During the MoD squad meeting, when Polly takes a bite of the pie she messes the cheese up, but in the next scene it's fine. Also, when Nick sees the cheese on top of the pie it is not melted, but when he pauses to think and stares at the pie, the cheese is clearly melted around the edges.
When Nick's ex-wife and son visit Nick after the Heather Holloway article, he first talks to his wife from behind his closed door. At this time he has stubble on his face from not shaving. When he answers the door - and for the rest of the scene - he is clean-shaved.
When Polly is arguing with Nick about cigarettes and alcohol,
in one shot her hair is tucked behind her ear. Then in the next shot her hair is covering her ear. Then in the last shots of her, Polly's hair is tucked back behind her ear.
During the MoD squad meeting, when Polly dips a piece of bread in her food it is a short piece of bread. She lifts it to her mouth and it is a new long slice. Next shot (seen from the side), it's short again.
During the second MoD squad meeting when Bobby Jay is talking about the Boeing pilot, Polly's right hand is on the table and her left hand is high and empty. Change of camera angle and we see her lower a glass to the table.
In the scene where Nick is riding in the Rolls-Royce with Robert Duvall, there are at least three different Rolls-Royces used. In the first shot of the exterior of the car, we see a standard Rolls Royce Silver Cloud in profile. In the interior scene(s), it is clear that there is an opera window in the "C" pillar behind Duvall. In the last exterior view of the car, it's clear that the same "C" pillar had no opera window in it and there is no rear door quarter window as there is in the first shot of the RR's exterior and the roof profile is entirely different in the first and last exterior shots.
When Heather watches Nick on TV, out the window is a sky-scraper. No such structures exist in Washington, DC, because of building height restrictions. Director Jason Reitman points this out in the commentary.
The owner of the tobacco company in this film is addicted to tobacco. But in real life, the Big Tobacco bosses and owners don't smoke or use the stuff that they sell to others! (They are whom Nick actually represents in the film.)
During one conversation it is stated that Nick's used to be a quarterback for the (Boston) Bruins. The Bruins are and ice hockey team, not a football team. For this statement to have the same meaning the team would either needed to be changed to the (New England) Patriots or the position changed to an equally important one in ice hockey.
When Nick asks Jeff if lighting a cigarette would blow up in an all oxygen environment he responds "probably", his response is only speculation not based on fact because he has no experience in physics, chemistry and astronomy.
The Captain's funeral is held in Winston-Salem, North Carolina. A limos has a bumper labeled TCP-54321. Transportation Charter Party is a uniquely Californian designation issued to limos by the CA Public Utilities Commission.
When the tobacco industry agree to pay $256 billion, the courtroom clip on the screen shows the trial of Larry Nevers and Walter Budzyn, Detroit policemen accused of murder in the death of a man named Malice Green in 1992, which is fairly iconic footage in Detroit history.
In hospital, Nick is shown with an IV hooked up to a machine on a pole behind him. The machine, however, is actually a tube feeding pump, not an IV pump. There also isn't any tubing on it, or feeding solution, or IV solution.