After a certain period a crime is considered spent and you can not be required to reveal it - except in some very limited circumstances. You'd have to reveal spent crimes if you want to join the police or become a magistrate for instance. You might want senior politicians added on this list perhaps.
If you got a fine or a short prison sentence, the period is relatively short. A long prison sentence for a serious offence is never considered spent. I think there is something of a sliding scale of how long a sentence takes to expire.
I would want essentially the same from the right to be forgotten. A citizen should not have to see Google reminding potential employers of a minor or youth offence 20 years ago when the legal system feels it expired ages ago.
Doesn't seem that complex to achieve either. So what would be the problem then?