How Would You Deal With A Difficult Customer Who Says That You Have Sold Them A Faulty Product?

First try to make him feel at ease , then listen to what actually has gone wrong and try to convince the customer without being harsh and be polite always with the customer.

I would apologize to the customer , letting him know that if the product is faulty it isn't the store's fault but the manufacturing company.  I would let him/her know that I will do my best to refund the money or get him a new one that works and try it for him there. I again would make sure that the customer is happy when they left the store .