What is the biggest mistake one could make in customer service?

lying

Over talking.

when you say, we dont have this, we can't do that, or its not available to a single customer demand..

Not getting the basic point of customer about his/her need..

Refusing to listen to a customer's concern

Not listening to the customer as well as disagreeing with the customer is a biggest mistake one can make.
Even though the customer is at fault ignoring their talks is the biggest drawback even for an existing client.

well, I believe that there are, in fact, mistakes ont only one mistake.
For instance, one should avoid: lying to customers, not respecting deadlines, not answering their queries and request, and not accept their complaint and show understanding

when you talk to customer before you listen its the biggest mistake