Factual error: Fairfax was not present at the trial of Charles I, although his wife Anne was, (and was forcibly removed after telling the court what she thought of them).
Factual error: Fairfax didn't become a member of Parliament until 1654, long after he is shown sitting and voting in the film (in 1647).
Factual error: Denzil Holles was never Speaker of the House of Commons.
Factual error: Although he did support the execution of the King, Henry Ireton was no sanctimonious Puritan bigot, but a moderate and a talented general. He was also Cromwell's brother-in-law, not his cousin.
Factual error: Thomas Fairfax did not succeed his father as 3rd Baron Fairfax until 1648, yet Charles I talks about the day long ago when he became a lord. He also refers to him as Lord Thomas. This would make him the younger son of a duke or marquess, not a baron in his own right. He is Lord Fairfax and only Lord Fairfax. A king would most definitely know this.