Can a used car buyer get his money back for a problem with the car that he didn't notice until after the purchase?
Based on used car law, if your agreement has gone through and you fulfilled the terms of what you told the buyer, he generally may not sue you or get the money back. In most cases, a used car purchase sold between private individuals is an "as is" transaction with no warranty or guarantee implied by used car law. Thus, unless you gave him an express warranty about the issue he is raising, or unless you lied to him in some way or coerced him into buying, under used car law, he is generally not going to have any legal justification for suing you based on the transaction.
While most used car sales are "as is" transactions, sellers do have some obligations under used car law. The main obligation that you have as a seller in many states is to disclose whether the car is a salvage vehicle, meaning, was it ever in an accident and declared a total loss? If the car in question was not repainted because of an accident and doesn't have a salvage title, based on used car law, the buyer can't require you to take it back based on the fact that it was painted.
Based on used car law, the duty here is on the buyer to inspect the car, ask his questions, and make sure the car meets his needs up front, before the transaction takes place. Because he didn't do that in this case and didn't confirm whether the car was painted or repainted, it is his loss that he didn't check and you're not going to have to give back the money or pay any damages if he does sue you. Based on used car law, he has no legal grounds based on the set of facts presented and his case should be dismissed if he tries to bring it.
To get a better understanding of used car law, you should consult with a lawyer in your state. In addition, you shouldn't try to handle any legal dispute, even a seemingly open and shut one, without professional legal advice.