First thing you want to do is use reputable carriers, or make sure your broker does. Specifically request that your carrier has a good reputation if necessary. Another preventative measure you can take is to look over the carriers insurance. You can request this from your broker prior to them booking the carrier. Make sure they have the proper amount of insurance necessary to cover your car entirely. An eight car hauler is required to be insured for at least $250,000 in damages, most carry around $600,000.
Next read over the Bill of Lading/Inspection Sheet. It will clearly say what the driver is responsible for and what he isn’t responsible for. Carrier negligence is always covered but bad weather usually isn’t. Read this paper carefully and get a copy on pick up. If the driver arrives and the car is damaged you have proof that the damage wasn’t there when he picked up the vehicle. If you don’t have the copy from pick up then the original may get altered and it will be impossible for you to get any sort of compensation for the damages.
So let’s say the driver arrives and there is a huge scratch on the passenger side of the vehicle. You will still want the car dropped off and you will still have to pay the driver for the transport. Contact your broker before you sign anything, they won’t tell you anything special but it will ensure that everyone is on the same page. Mark on the Inspection Sheet what kind of damage was done and get a copy of the Inspection Sheet/Bill of Lading with the damage marked on it. DO NOT SIGN THE INSPECTION SHEET UNDER ANY CIRCUMSTANCES, EVEN IF THE DRIVER THREATENS TO NOT DROP THE CAR OFF, IF YOU SIGN YOU WILL NOT GET COMPENSATED FOR THE DAMAGES EVEN IF YOU DID MARK THE DAMAGE ON THE INSPECTION SHEET.
Send a copy to your broker and they will take care of getting all of the necessary information to the insurance company. It will take a while but eventually all monies will be paid.