best way to statistically detect anomalies in data
Take a look at Control Charts, they provide a way to track changes in your data visually and specify when the data is "out of control" or "anomalous". They are heavily used in manufacturing to ensure quality control.
This question is impossible to answer without knowing much more about the particular data you have. For an overview of what kinds of approaches exist, see Anomaly Detection: A Survey by Chandola, Banerjee, and Kumar.
Bayesian classification might help you find some anomalies in your data, depending on the type of data and how good you train your Bayesian filter.
There is even one available as a web service @ uClassify.com.