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.
During the MoD meeting, Bobby is shown wearing a tie with a very distinct pattern; in a later shot, his tie doesn't match.
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 Nick is giving the stats of how many people cigarettes have killed, the 1 appears in the millions place before the scrolling numbers hit 999,999.
After Nick testifies before the Senate committee he leaves his son Joey in the hearing room. When Nick steps out of the building Joey is inexplicably at his side.
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.
During one conversation it is stated that Jeff used to be a quarterback for the Bruins. This is not a reference to the NHL team (Boston Bruins), but to the NCAA Football team (UCLA Bruins).
When Heather Holloway drops the files while watching TV footage of Nick discussing her article, the computer monitors on everyone's desks clearly have no cables plugged into them, making them useless.
When Nick and his son wait for Jeff, his assistant Jack comes in and greets them with the question "Are you jet-lagged and all, it's like 2 in D.C. right now." They are in Los Angeles for the meeting where it would be 11pm in that case, however the whole scene takes place in broad daylight. Therefore there is no way that it is night time in Washington D.C. right now.
When Bobby Jay Bliss enters a National Guard recruiting office in 1971, modern cars are reflected in the door.
Nick is shown flying from Washington D.C. to Greensboro, North Carolina (the airport closest to Winston-Salem) on a wide body jet. No wide body has served this route since the 1970s.
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.
During a meeting of the "MOD" squad, Polly Bailey mentions her upcoming appearance on Dateline NBC (1992). 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.
When Nick and Heather are having wine, the wine steward pours the very last drop into the glass. No respectable steward would empty the bottle entirely into a customer's glass as bitter sediment settles to the bottom.
Heather's eyes are brown throughout the movie, but when Billy first describes her to Nick he says she has blue eyes.
Polly Bailey, is introduced on the cover of "Daily Drinker" as "Mother Burgandy," a common misspelling of "burgundy".
Jeff Megall and his agency would be able to sue Nick Naylor and the Academy of Tobacco Studies for disclosing their private conversation to a reporter.