This movie is a remake of the German "It Happened in Broad Daylight" (1958). Several critical changes in the story have been made. In the 2001 version, Nicholson loses his marbles, he doesn't tell the bait's mom what he's up to,and we do not ever see the killer (originally Gert Frobe). In 2001, we do not see the killer's fate (death) via the police and a chase as in 1958. Instead, he dies by an auto accident. These changes reflect the greater modern adherence to crazy states of mind or downgraded rationality and a greater importance assigned to random acts as opposed to human attempts at control.
The transition of Nicholson from a normal retiring cop to a half-crazed man is not handled well via the plot, but it is handled if clumsily, and also it's done valiantly by Nicholson. He cannot be faulted. He doesn't go the extreme of The Shining. He does inhabit the character. The movie is overlong and gets sluggish. It doesn't generate the suspense it should. It is overblown in certain respects. I think that Sean Penn in his 3rd movie directing outing needn't to get a much better handle on the developing madness of Nicholson, because that is what this new story is really about. The serial killer and the little girls almost become an accompaniment, especially since we do not see the killer.