The film itself is basically a premake of Zodiac. The two films have a lot in common-based on true story, a killer shooting people at night in cars, amateur 'investigation' by writers, the focus of the movie shifting from uncovering the killer's identity to the effects of this investigation on the investigators, a lack of clear resolution. One of them's a bit better than the other, though (I won't explicitly say which, but if you mount your own amateur investigation over the next few minutes you should be able to infer which film I prefer).
One of the big differences between the films lies in the process of investigation depicted (which is why I used inverted commas above). Zodiac's Robert Graysmith (Jake Gyllenhaal) tracks the Zodiac killer over several years, with the case gradually consuming his entire life. Monster's Andreas, played by Leonard Mann, begins the film by resuming work on a previously-abandoned book about the serial killer terrorising Florence. In an early conversation with an investigating officer, he's told to take advantage of the scope for imagination afforded by his job, and he certainly takes this advice to heart. Eschewing the fact-centric approach traditionally taken by murder investigations, Andreas spends the rest of the film building a Freudian profile of the murderer in his mind, constructing elaborate backstory and motives for the killer based on No Evidence Whatsoever.
Although, there may be some evidence after all-Andreas draws a picture of what he thinks the killer may look like, which is pretty much a self-portrait (and both he and his girlfriend agree on this). He seems sexually distant from said girlfriend (the fool; she's very nice-looking), and his 'imaginary' killer is impotent. Also, his killer's imagined home is filled with large versions of a wooden figurine he has on his own desk. In short-he's either the killer, or his psychological profile of said killer is highly autobiographical; in effect he's investigating his own life and childhood by proxy.
This latter explanation is the more likely, and marginally more interesting, of the two possibles. However, Leonard Mann isn't a good enough actor to really captivate, and even at that he's not given enough to do, so the film becomes nothing more than a load of shots of him looking constipated, a parade of anonymous people being shot and cut up, and a too-on-the-nose-Freudian-to-be-true reconstruction of the killer's burgeoning mother issues. A black and white trial sequence towards the tail end of the film brings most of the characters together to gaze at the person who's ruined all their (imaginary) lives, and ends with a judge stressing the need to understand the killer's life, and not just cast him out of society. This desire to understand chimes with Andreas' need to get to the bottom of the killer's/his own neuroses.
Because Mann spends the film reinterpreting (or reliving) past events, there is little or no tension to any of the murder scenes. The first such scene, which opens the film, does take place in the 'present', and achieves a reasonably evocative atmosphere, even though the audience is denied any chance to identify with the victims, seeing them as no more than silhouettes in a tent before the killer goes to work. The lighting, camerawork and editing throughout the film are consistently impressive, even if the framing and music are fairly bog-standard, nicely complementing the acting. Gabriele Tinti, who was obviously pouring all his energies and youth into his marriage with Laura Gemser, turns up in a small supporting role looking near-unrecognisable.
As I said, Monster is one of those gialli that thinks outside the box. I'd hazard a guess that the director saw it as a more of an arty thriller, but he does frequently draw upon imagery typical of the genre, and the amateur investigation aspect secures its spot in the pantheon of gialli. Its unusual approach, which it shares with another based-on-a-true-story giallo, The Pyjama Girl Murders, is to be commended for effort. In terms of execution, and watchability, however, neither film hits the spot. The execution of both is po-faced and methodical, and I like funner, messier executions. In my films, anyway.
(Zodiac's better, by the way. That last paragraph has inspired me to avoid an open ending of my own.)