1. Give them the backstory.
Often, the reason behind a new product or feature never flows down to Support or other customer-facing teams. When they understand the internal motivation: the use cases that warrant a feature's creation, the potential benefits to new or existing customers, or internal factors which necessitate a change, they are able to perform engaged support, and provide better answers. Just because you know the feature is worthwhile, doesn't mean the front lines do. When someone puts a stack of work on your desk, don't you like understanding why?
2. Let them buy the customer a figurative drink.
As a waiter in my mostly-forgotten twenties, I had some great managers. They had enough trust in us to know when to buy an upset customer a dessert, a drink, or comp the whole table's meal. They never questioned us, and we never abused it. Setting the parameters to allow your support staff to say, "I know that must have sucked," will go further than "I see you are frustrated, I am very sorry." A one time credit, a temporary upgrade, or other small gesture turns a negative experience into a relationship-building one.
3. Support your product's documentation as well as your product.
Docs are aren't the answer to all technical issues, but they are a common destination. If a feature needs a doc, and that doc doesn't get the user up and running, why bother writing it? Ask for Support's guidance regarding documentation and training to insure people are using the product and the documentation the way you think they are.