If I mistakenly caused a very minor scratch on a car what does the Halacha require?
A person is obligated to pay for any damage he caused even if it was by mistake (see Shulchan Aruch Choshen Mishpat 378, 1). You should find out if there is any damage in such a scratch and in such a vehicle. The same minor scratch can be considered as damage in a case of a shiny new car and not considered damage at all in a case of an old and worn vehicle. In case where the scratch caused depreciation of the car, one should find out how much he is required to pay for the damage, because payment for damage is estimated by depreciation of the object as a result of the damage (Shulchan Aruch Choshen Mishpat 387). Nevertheless it seems that in this case of a minor scratch on a car, the cost of repair and the vehicle's depreciation will be more or less the same.