Mr. Harvey is a sexual predator, a rapist, a serial killer. He's the 36-year-old neighbor who rapes and murders Susie, within minutes of her own home. Although indispensable to the novel, his story is always secondary to the stories of Susie and her loved ones. After Mr. Harvey leaves Susie's suburban neighborhood, she doesn't watch him as closely, unless he's thinking about Lindsey, or moving back toward her family. Susie is subtle but clear that he carries on his brutalities after her death, but if she sees his hideous acts, she doesn't do much reporting back on them.
It's a much-noted fact that Harvey is revealed as Susie's killer from the first pages. This is a powerful use of dramatic irony. The readers are Susie's confidants, privy to the secret she wishes wasn't secret. We watch along with her in suspense for Harvey's guilt to be made known. Susie's constant use of the title "Mr." to refer to her rapist is disconcerting, but it pushes home the point that she viewed him as an authority figure, someone to be trusted, and if not trusted, obeyed.
"According to the experts, there is no common thread tying serial killers together—no single cause, no single motive, no single profile." (source: FBI report on serial murder)
Susie can see into Harvey's past and she tells us some of what she sees. We learn that his mother was a desperate woman who taught Harvey to shoplift and even rob victims of roadside fatalities from alongside the road. At some point Harvey's father abandons his mother in Truth or Consequences, New Mexico. His family, before and after his mother disappears from it, seems pretty transient.
As a kid, Harvey is ashamed that his father doesn't have a 'normal' job. He can't tell people that his father "[works] in the desert [building] shacks of broken glass and old wood" (8.3). Still his father passes along his knowledge of building to his son. We can see that Harvey's father is an abusive person, but aren't given details.
We can say, with certainty, that Harvey's childhood was almost the complete opposite of Susie's. In Harvey we see a yearning for an idealized home, and family, in his chosen profession: building dollhouses, idealized homes in miniature. His success gives him what his father's building couldn't, financial security. Harvey makes enough to buy that family home in the suburbs, but he has no intention of filling it with a family of his own. Rather, it becomes the disguise which allows him to infiltrate the world he covets.
There are lots of allusions to Othello in the novel. Othello, unlike Harvey, is a largely sympathetic character, whose jealousy is fanned by the evil Iago, until he allows it to overcome him, and he murders his beloved wife. Since none of the other characters in The Lovely Bones exhibit jealousy or murderous tendencies, we can think of the allusions as clues pointing to jealousy as a motivator for Harvey's hideous behavior. He can't have the idealized, loving home and family, so he builds structures that allow him to infiltrate and attack it.
Mr. Harvey's been living in the neighborhood for a few years at least, and Susie seems to be his first human victim from the neighborhood. According to Susie, Harvey's been staving off his urges by killing cats and dogs. In the novel, the phrase "serial killer" isn't used, because in the early '70s, it hadn't yet become a part of the popular vocabulary. We call him a serial killer because he fits the usual definition. As opposed to murderers and spree killers, serial killers are known for having 'cooling off times' – time in between attacks. Attacks are risky, big events, not every day happenings.
If the list of the dead we get in Chapter 14 is complete, Harvey kills a woman and a girl in 1960 (when Harvey would have been about 23), one girl in 1963, a teen girl in 1967, a teen in 1969, another teen girl in 1971, and then Susie in 1973. We later learn that "The first girl he hurt was by accident" (21.100). Susie tells us that, "He had regretted it, this quiet muffled rape of a childhood friend, but didn't see it as anything that would stay with either of them" (21.100).
We aren't given many details about Harvey's post-Susie victims. But when Harvey visits the shack in Connecticut in 1981, we are told that he killed a "young waitress […] several years before" (21.1).We notice that there are years in between most killings, and other than 1960, no more than one killing per year. These gaps between killings are part of why Harvey is able to avoid detection.
If we examine the list of the dead in Chapter 14, we can also see that other than Sophie a landlord/lover, his victims were first very young girls, then progressively older teens, and then the waitress.
But, you'll have to make what you want out of that. We don't have enough reliable information or expertise in serial killers to make a whole lot out of the information. Plus, we have to be careful using anything we read about Mr. Harvey to generalize about actual serial killers. Otherwise, the FBI might get upset with us. The FBI says,
Serial killings are rare, probably less than one percent of all murders. They do, however, receive a lot of attention in the news and on screen—and much of the information out there is wrong. Yet, the public, the media, and even sometimes law enforcement professionals who have limited experience with serial murder, often believe what they read and hear. And this misinformation can hinder investigations. (source)
Susie tries to show us that Mr. Harvey might be clear and calculating in his attacks on girls, but doing these acts isn't something he can easily deal with afterwards. She even comes to believe that he tries to stop himself – one explanation for why there is some time between attacks. Of course, he never tries to get help, or anything like that. Susie doesn't ever make excuses for what he does, but she does try to show us some of what goes on inside his head.
Interestingly, one thing that pushes him to strike again is his dreams. So long as he's having dreams about beautiful buildings, like the ones he has after a kill, he can keep the urges at bay. But, then the "not still dreams" (8.2) in which his desires to hurt women and girls come out, and the urges come back.
When we see Mr. Harvey eight years down the road, he has deteriorated further. Susie says that the "edges of Mr. Harvey seemed oddly blurred" (21.91). He no longer has a fixed residence, a stable profession. He no longer has a disguise of normalcy. Somehow, he's been able to block off "the memories of the women he killed but now, one by one, they were coming back" (21.9), though he doesn't yet remember Susie.
Strangely, he sure remembers Lindsey though. If it hadn't been for her, he might've stayed there in the neighborhood for years to come. So, she's become as symbol of threat. Dreams and memories of her also seem to be the catalyst for his renewed memory.