Long ago I bought a car. I had horrible credit at the time and everyone was wanting to charge me interest in the 20 to 23% range.
I finally found a car and the dealer set me up with a loan that was normal 8%,going rate at the time.
fast forward a week or so. GMAC called and the lady said there was no way they could sell me that loan at that rate.
I just told her that I was looking at a contract signed by one of their agents, she then tried to deny that the dealer was acting in the capacity of their agent. Couple of days later one of her superiors called with the same spiel. I told her the same thing. Never heard another word!
OP pointed out their error not once but twice. The dealer and the lender have many more resources than the customer and should have corrected the error that OP pointed out.
I would repeat the advice go talk to a lawyer. The dealership is either dishonest or incompetent, neither of which is the OP's problem!