There are leaps, not necessarily inexplicable ones, that could have benefited from at least passing explanation. One possible theme is that Nicholson's cop is supposed to be a figure of soiled integrity, an aging Bogart adrift in a shallow world. I made a promise. Aging, and generational divides, appear crucial to understanding his quest. When the girl's body is recovered, Nicholson is already at his retirement party, but insists on traveling from Reno into the mountains to have a look at the case.
Retirement can be a killer, especially for a man alone.
And a little old-fashioned checking finds that the suspect was doing time during the town's previous child murder. Like many old people, Nicholson is frustrated from being patronized at best, ignored and ridiculed at worst. He sometimes sputters with anger at not being taken seriously. The Pledge is several cuts above the usual serial-killer fare, but its loose, rambling construction creates its own frustrations. Maybe it will all make sense after the third or fourth viewing.