Bruce Schneier has a great op-ed on CNN on why it's stupid to talk about whether the FBI should have "connected the dots" on the Boston bomber. As Bruce points out, it's only in hindsight that there's a neat trail of dots to connect, a narrative we can make sense of. Before the fact, it's a hairy, swirling hotchpotch of mostly irrelevancies, and it's only the "narrative fallacy" that makes it seem like a neat story in retrospect. The risk here is that intelligence agencies and the press will push this fallacy as grounds for taking away more rights and more privacy in order to "connect the dots" next time.
Rather than thinking of intelligence as a simple connect-the-dots picture, think of it as a million unnumbered pictures superimposed on top of each other. Or a random-dot stereogram. Is it a sailboat, a puppy, two guys with pressure-cooker bombs or just an unintelligible mess of dots? You try to figure it out.
It's not a matter of not enough data, either.
Piling more data onto the mix makes it harder, not easier. The best way to think of it is a needle-in-a-haystack problem; the last thing you want to do is increase the amount of hay you have to search through.
The television show "Person of Interest" is fiction, not fact.
There's a name for this sort of logical fallacy: hindsight bias.