If the umpire calls you out on two strikes, that is an error of law.
If the umpire thinks the ball is over the plate and it isn't, that is an error of fact.
For example, if a person defends himself with a knife from an unarmed attacker because he believed he was justified in doing so to protect himself from great bodily harm. By legal definition, the defendant made an error of law if his self-defence belief was not also "reasonable" and if the danger was not imminent.
An error of fact will be when a person hits someone in a bar thinking he was the one who was about to attack him, but it was his friend next to him who was the aggressor.
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Take a statutory rape case. An error of fact is that everyone believed the victim to be 16 years old when she was in fact 18 at the time of the incident.
An error of law in the same case would be a court's belief that statutory rape can be an act between two 18 year old people.