In one scene in the White House, a close up shows a door with a contemporary lever instead of a doorknob. The type of lever shown wasn't used until after the passage of the Americans With Disabilities Act of 1990.
The helicopter that almost lands on the roof of the McGraw-Hill building in 1971 is clearly an AS350. The original, single engine version of this did not make its first flight until 27 June 1974. The twin engined model used in the movie did not fly until even later.
As Irving first researches Hughes for the hoax, he picks up an edition of Newsweek bearing the title "The Secret World of Howard Hughes," and dated 1971. He actually has the April 19, 1976 issue of Newsweek, which was printed after Hughes's death and included a sketch of Hughes during the last few years of his life.
McCullough congratulates Irving on the authenticity of the manuscript by citing a conversation he had with Hughes that he didn't tell anyone else. However, this conversation was noted in the Newsweek article on Hughes.
About 12 minutes into the movie before Irving is to meet with McGraw Hill, there is a southerly view of Manhattan with the Empire State Building in the foreground. In the distance looking toward lower Manhattan are the buildings of the World Financial Center. These buildings did not exist in 1971. Also, in 1971 the Twin Towers of the World Trade Center would be visibly under construction albeit not very tall at that time.
A document in one of the files sent to Irving states that Howard Hughes loaned Donald Nixon, brother of Richard Nixon, $205,000 in 1956 to secure Pentagon contracts; Irving concludes that this information will bring Richard Nixon down if made public. In fact, the loan was to help Donald Nixon save his restaurant chain, and became public knowledge during the 1960 presidential race.