Design a system capable of tracking bad request down quickly

Say your system are expected to serve 100 billion requests per day on average,
one day, a user complains that his client shows that one request failed,
he wants you to help track the bad request down.

How should you design such a system that is able to give the result to the user as quickly as possible.

Note: You should consider scalability, imagine that you could possibly have hundreds of servers spread across tens of datacenters.