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).
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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. See more...
Cromwell mistakes
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.