Make sure to check that your auto mover is licensed and registered with the Department of Transportation. If not, this could present problems regarding the coverage of you car.
If you are transporting your vehicle internationally, you should check with U.S. Customs what documents you need to obtain. You might be required to provide the original title or certified copy of the title. If the move requires shipping your vehicle by ship, you might need marine insurance to cover the car as it physically crosses the ocean. More information on professional mover here.
If you have unresolved disputes regarding your service, always try to work out your dispute with the auto mover first. They often work on a referral basis and are motivated to working out problems. However, if you feel you have reached a dead end or that you have not been treated reasonably, you have the option of filing complaints with multiple agencies (BBB, State and or Federal Department Of Transportation, Interstate Commerce Commission) as well as seeking legal counsel.
When choosing a mover verify his license with your local DOT office. very moving company has to be licensed and insured. There are different types and levels of licensing, and the rules are different from state to state.