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.
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.
When Johnson reads the letter from Lincoln at his trial, he says it came from the "White House." At that time, it was called the Executive Mansion. It was Teddy Roosevelt who officially first called it the White House.
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 song "Red River Valley" was not written until after 1868.
Several scenes include the use of 48-star flags, not introduced until 1912.
Johnson is given John Wilkes Booth's calling card, throws it down and says "No, I don't know the name." But Booth was the most famous actor in the country, even before the Lincoln assassination. To not know the name Booth would be tantamount to someone in the 20th Century not knowing the name of John Wayne. And Booth was certainly well know through Washington, DC during the Civil War. It is certain that Johnson would have been very familiar with the name John Wilkes Booth.