Factual error: Sir Thomas Fairfax was in overall command of the New Model Army not Cromwell. He was in charge of the cavalry on the left wing (the Ironsides).
Factual error: In the scene where the king attempts to seize the five members from Parliament, Cromwell makes a dramatic refusal to leave and proposes various "Laws" to prevent his arrest. Cromwell was not one of the five members whom the King tried to arrest and no law can come into force until it had been signed by the reigning Monarch anyway.
Factual error: In the scene of the Battle of Edgehill (the first battle in the movie) Cromwell utters the famous "Oh Lord, Thou knowest this day..." prayer. This was, in fact, said by Sir Jacob Astley one of the Royalist Generals on the other side. It is also unlikely that Cromwell was even at the battle.
Continuity mistake: At the battle of Edgehill when Crowell's cavalry and Prince Rupert's cavalry are in the middle of a melee and you can see a wound on Crowell's left arm, the same wound he receives at Naseby. It is clear that the scene was meant to be used for the battle of Naseby but was cut and used at Edgehill.
Factual error: Halfway through the film, Cromwell decides to create the New Model Army, and he kits them all out in dark brown uniforms. In fact, Cromwell's New Model Army wore red coats, (cheapest available colour), and this was the reason the British army wore red until the late 19th Century. In the movie, King Charles's troops all wear red; in fact each different regiment wore their own coat colours, blue being a popular choice.
Factual error: In the last battle, Naseby, the Parliamentarians are shown to be outnumbered by the Royalists. In fact it was the other way round (13,000 to 9,000).
Continuity mistake: Peers and commoners (like Cromwell) are seen sitting in the same chamber in Parliament. In reality, of course, the Houses of Commons and Lords are separate chambers.