How will you detect KPI inaccuracies when basic statistical data is fudged or misreported in a very fast-paced environment?

There are some signal processing techniques and learning algorithms that can be used to find unordinary data or trends in datasets. Kalman filtering can be used to compare something such as data appearing on a general ledger with monthly expense reports coming from an individual or department to find such misreported information. 

You can learn more here: 

http://en.wikipedia.org/wiki/Kalman_filter