When Cromwell trashes the "Catholic" golden ornaments inside the church, the priest's collar changes.
In the scene where Cromwell hangs the officer for treason in the soldier's camp, a long shot of the deceased officer's body hanging from the rope shows his mouth to be open. A close-up of the officer's face moments later reveals that his expression has changed and his mouth is now closed.
Cromwell was not one of the Members of Parliament named for arrest in the King's warrant. Cromwell was not present in Parliament at the time the King and his troops entered the House of Commons.
Hyde is called 'Sir Edward Hyde' and addressed by the Queen as 'my lord' in scenes which take place in 1641: he was not knighted until during the Civil War and not elevated to the peerage until 1661.
Cromwell's dismissal of the Rump Parliament happened before he was offered the crown, not afterwards.
Henry Ireton is shown heading the parliamentary deputation who offer Cromwell the crown. Parliament's offer happened in 1657, by which time Ireton had been dead for 6 years. Furthermore, the scene suggests a personal falling-out between the two men, who in reality were particularly close (Ireton was Cromwell's son-in-law).
Edward Hyde is shown giving evidence at Charles I's trial;
the trial happened in 1649, by which time Hyde had left the country.
At 1:38:48, when one of Cromwell's officers is hung and his body slowly turns to the camera, a metal wire is visible running from the hangman's knot to the collar of the man's jacket. This connects the actor's chest harness to the rope so he's not strangled.
When Prince Rupert yells "Tally Ho!" as a battle cry, this was at least one century before the phrase (which is derived from the French hunting call "taïaut") had entered the English vernacular.
The Prince of Wales calls Prince Rupert "majesty" at the battle of Edgehill.
As a prince, Rupert would be called "your highness". Only a king is addressed as majesty.
Prince Rupert appears at the Battle of Naseby with his poodle Boy. In reality Boy had been killed at the Battle of Marston Moor, the year before.
The Battle of Naseby is shown in an area with high hills in the distance. The reality is that part of Northamptonshire and Leicestershire borders are fairly flat. The nearest hills to what is shown in the film would be Bradgate Park to the west of Leicester or the area that is now the Hollowell Reservoir to the south.