It detects anomolous patterns that make utterly no sense on the surface level.
It is already used by catalog companies who on phone orders present you at the end with "specials" that the computer whips up just for you. Their acceptance rate on customers buying the spur of the moment "specials" has gone from under 10% to about 75% since they have begun using advanced algorithms which make seem to make no sense at all. That's just one example of how Mad Ave uses this technology to target specific consumers, and now this govt agency wants to take it to entire new levels in the war on terror.
The problem is integrating all of these different databases. That's a nontrivial problem. The next problem is the government being at all effective in putting those algorithms together. I just do not see that happening on as subtle a level as you describe.