During the roll call vote on Leffingwell's nomination, as the Majority Leader walks up to the Vice President to tell him the vote will be tied, senators can be heard responding yes or no to the nomination. Although he is not seen in the shot, the name of Senator Strickland (played by actor Will Geer) is called and a voice answers "No". But that voice is clearly not that of Geer, whose voice is heard responding immediately after when the name of Senator Sundberg is called. At that time, a voice which is unmistakably Geer's replies "Nope".
When the scene where the tour guide is talking about Lt. Grant and Lt. Lee in the Mexican War, he states that they were classmates at West Point. They weren't. Lee graduated 2nd in the class of 1829 and Grant graduated 21st in the class of 1839. Also during the Mexican War Grant indeed was a lieutenant, but Lee by at this time was a captain.
When Senator Brig Anderson (Don Murray) returns home after the black-tie party, he enters his bedroom and removes his tuxedo jacket. An undershirt is clearly visible under his dress shirt. He then goes into the bathroom and removes his tie, but having awakened his wife, comes back into the bedroom before taking off his shirt, at which point, he's no longer wearing an undershirt.
Herbert Gelmen (Burgess Meredith) testifies that he lived at 2714 Carpenter Street while attending the University of Chicago. In actuality, that address is actually the address of St Mary of Perpetual Help Catholic Church, and neither a residence nor a fire station.
Certain errors are made in the way senators are usually called upon or addressed in the Senate chamber. In the film, senators are almost always referred to as "The senior (or junior) senator from" a state, but in fact the terms senior or junior are seldom used in recognizing or referring to a senator on the floor or in committee. Also, when Senator Lafe Smith is called on during the climactic roll call and at first doesn't answer, the clerk repeats his name, at which point he responds "No". But in actual Senate practice a senator's name is not called a second time until after the initial roll call has been completed.
Senator Kanaho, the Senator from Hawaii, is shown seated on the minority side of the aisle in the Senate chamber, but in the subcommittee hearing on Leffingwell's nomination he's sitting with the majority.
Senator Brigham Anderson of Utah is shown in his home drinking from a distinctive fluted Coca-Cola bottle. Anderson (from his first name and home state) may be a Mormon; the novel states this explicitly, but the film does not.
Until his elevation to the Presidency, Vice President Hudson is not shown traveling with Secret Service protection. Since 1954, such protection was provided unless specifically declined. Also highly unlikely that a sitting Veep would be traveling alone on public conveyances such as commercial airliners and taxicabs, as shown in the movie.
Vice President Harley Hudson casts the tie-breaking vote on the Leffingwell nomination after he is informed of the president's death. Under the Constitution, the vice president immediately becomes assumes the presidency when the president dies. Therefore, he is no longer the presiding officer of the Senate and could not legally cast a tie-breaking vote. This mistake does not appear in the original novel.
When the roll call vote is being conducted on the motion to advise and consent to Leffingwell's nomination, Senator Van Ackerman's name is not called. Even though he had left the Senate Chamber, the clerk would still have called his name.
As the security guard enters Senator Anderson's office the telephone is ringing. The rings (apparently added in post-production) each echo around the office, but the final ring stops abruptly and there is no echo. Even if the caller had hung up in mid-ring, that ring, like the others, would still have briefly reverberated around the room.