Actually the film is in places very accurate.
The trial scenes are almost word for word accurate for example.
The exploding cannonballs are are common enough error to be forgiven.
For a list of general inaccuracies I suggest you read good ole Wikipedia. It's a pretty fair list.
Cromwell and Charles were both complex characters, men of their time etc but they were both pretty awful human beings.
Charles' dad was pretty screwy too. Sitting in on the torture of poor Agnes Sampson and others.