people take that lowball money offer and never fix the car. You'll have to call them on their bluff and tell them to fix it. This is when they'll tell you it's actually totalled and can't be fixed. Next they will find low-end comps of a car the same model/year/miles and see what they are going for from used car dealers. Then they'll add the cost of tax and registration fees to that offer. You should find your own comps that are as high as possible as well to counter their offer.

You won't get anything for hassle factor (except maybe they'll provide a rental car), and they won't give you anything for mental trauma or bumps or bruises unless someone went to the hospital or doctor right after as a result of injuries sustained in the accident.