I'm sorry to beat a dead horse, but I had a couple of arguments against your initial post that I still find valid, and that haven't been made yet. So please, pardon my late and probably obsolete commentary. My points are two:
1) While you were arguing for the 'safety of your children,' you don't see that the only threat against your children is being abused by the neighbours. They could just as easily be abused by the state. Given your (hypothetical) 15-year old daughter posts nude pictures of herself on the Net (as it is pretty common, I hear) your (hypothetical) 18-year old son decides to have sex with a 16-year old class or school mate or any other relatively innocent action. You would consider the first a 'parenting problem' I guess, but not the police officer/judge. They would put your children on this list, and that's were their names will always be. Googleable, on the list. Is this protecting your children? Maybe they won't be raped, but they will carry a mark of shame — their entire life long.
2) As a European, I am so totally shocked at how Americans can villify people on the sole basis on their past. Say, a person has some sort of mental disorder, or any other kind of illness or social circumstance that played a large part of their decision in, say, raping a woman. They've been to jail now, they're on meds now, they're trying to immerse into society. Trying to be normal people. The sex-offender list is the best way to prohibit just that. They won't get a flat in a decent neighbourhood, they will have a hard time finding a job. But without these two premises, how they ever going to change? Living in a shoddy neighbourhood, working on a shoddy job, how are you going to not believe that you are a social outcast, that this society has done nothing for you, and you owe it nothing in return? In essence: this will make rehabilitation for them so much harder. Thus, instead of becoming functional members of society, they stay sick; maybe their mental disorder will grow worse, and then they're not a time bomb in your neighbourhood. They're off the leash in your entire town.
The key to safety is rehabilitation of ex-criminals, and making them feel like a member of society again. Not demonizing them and putting them on a social landfill.