Is it a problem if i let someone else drive the car without first listing them as an additional authorized driver?
Yes, and it can be a big one. If someone else drives the car without the Rental Companys permission, you have most likely violated the contract terms and any protection you had under that contract may be voided. This violation could complicate or even negate claims against your personal insurance and negatively impact any coverage you receive from your credit card. If the police stop an unauthorized driver, that driver can be detained or even arrested because they dont have any legal right to have possession of the car.