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Factual error: 26,000 people work in the Pentagon. If they were to all file past one person so he can try to pick out a crime suspect, and each person takes just two seconds to walk past, be checked, eliminated and sent on their way, it will take fourteen and a half hours to clear the building. There are going to be some very unhappy people at the back of the queue.
Factual error: The Pentagon is the largest office building in the world. It has seven floors, 28 kilometers of corridors and 620,000 square metres of office floor space. The idea that the entire building could be searched in one afternoon by six people is beyond absurd. If those six people could search an average of one office every five minutes and they worked twenty four hours a day, seven days a week they'd get through the whole building in 89 days and 15 hours. I don't think the punter they are looking for has a lot to worry about.
Factual error: At the inauguration party, the band sounds three "Ruffles and Flourishes" and then "Hail to the Chief" for the departure of the President. The President should receive four "Ruffles and Flourishes" prior to "Hail to the Chief", and both are sounded only at his entrance, not his departure.
Continuity: At the party where Kevin Costner meets Sean Young and Gene Hackman for the first time, and during the other early scenes, he's wearing the medal and ribbon for the Navy Cross - but he doesn't win the medal until later in the movie when he rescues the lookout during the storm, and this is what gets Gene Hackman to remember him (when he sees the story in the newspaper). He's too young and doesn't have the right other ribbons to have won the medal in Vietnam or any other action.