Answer:It really depends on the type of mistake the dealer made. The automobile sales contract specifies your and the dealership's rights and obligations under the agreement. Once the contract is signed, the dealer general rule is that the dealer cannot come back to you and demand more money from you and the dealer cannot back out fo the contract. Unless the dealer made a mistake that you were aware of, such as incorrect sales price, the dealer is probably stuck with the price that you agreed to pay.
In any contract dispute, you should be able to find an affordable attorney to review the contract to advise you of your rights before listening dealer. An informed consumer is an empowered consumer.