If I stole a priceless Stradivarius would I be punished any differently if in court I claimed to have thought it was just a cheap bit of wood with some strings attached?
Quite possibly. Intent often matters, e.g. involuntary manslaughter vs murder.
Quite possibly. Intent often matters, e.g. involuntary manslaughter vs murder.
As for murder, the penalties there do differ depending on your state of mind, but that's not an issue of mistake (you can't try to third-degree murder someone but mistakenly first-degree murder them).
Not to say I agree with the punishment in this case, though.
In the theft and criminal damages context, you could have an analog, though we don't currently, where being judged guilty of one of the more major theft or damages offenses (like "theft over $X") requires an intent to cause that level of theft or damages. If you meant to cause $50 in damages and actually caused $50k, that could be a lesser offense than if you meant to cause $50k in damages. You'd be found guilty of essentially "damage over $X but with intent to only cause damage under $X", the way 3rd-degree murder and manslaughter are lesser offenses due to the lack of intent to cause death, even when there was intent to violently injure non-fatally.
When you get excused is if you didn't act purposefully... e.g. if you drive your car recklessly and kill someone you'll be guilty of manslaughter. If you purposefully hit someone with your car you'll be guilty of murder even if you only meant to break a few bones.