I would listen to the customer's issue while also trying to bring the conversation to an area where we can have privacy in order to be fully attentive and also prevent a scene. If I can settle the issue myself, I would show empathetically that I am sorry for whatever situation occurred, and that I will be able to rectify the situation to the best of my abilities. If the situation is beyond my control or gets into uncomfortable territory, I would professionally (calmly but firmly) let them know that though I cannot personally fix the situation, I will put them in touch with someone that can.