I think it's certainly feasible to have technology that can aggregate vast amounts of data about people's activities from security cameras, communication systems, etc... The challenge is getting anything useful out of it.
What strikes me from watching "Person of Interest" is that the machine so consistently predicts impending dangers. That indicates that the programmer of the machine (presumably Finch) has a deep understanding of human behavior, and is able to convert that into algorithms the computer can use. I think that understanding of behavior is evident in Finch's other activity as well.