In his speech upon returning to the Senate after his presidency, Johnson says he had last stood in the chamber (as a Senator) in 1861. In fact, Johnson had previously served in the Senate until March 4, 1862, when he resigned, prior to being appointed Miltary Governor of Tennessee.
A key scene in the film depicts Johnson entering the Senate while it is debating his impeachment and removal from office, and making a major speech there in his defense. In reality, the actual President Johnson, despite his desire to confront his enemies in the Senate, never once entered or addressed that body during his impeachment trial.
The Vice-Presidential oath administered by the Chief Justice is incorrect (using the Presidential oath, adding "Vice"). In reality, the Vice-President's oath is the same generic oath taken by a Senator or Congressman.
The film erroneously portrays some historical aspects of Johnson's impeachment. The decisive vote against removing the President from office was cast not by an ailing Senator, brought into the chamber at the last minute, who has a sudden change of heart, but by a Republican Senator from Kansas, Edmund Ross, who believed the impeachment articles against Johnson were trumped-up political charges without merit. Also, the name of the Senator who would have succeeded Johnson had he been removed from office was Ben Wade, not "Jim Waters" as named in the movie.