anyone who has a Dakota Fanning fansite...

Generalizations.
1. Pedophiles (I'm American, not British) have a physical/mental/emotional attraction to prepubescent children; the legal definition has been expanded to include kids up to 13 although most of these kids are (clearly) pubescent.
2. Having a sexual attraction isn't a crime, which separates a pedophile from a child molester.
3. The majority of molesters are males 20-45, and include all races, socio-economic classes, and sexual preferences; female molesters are rare and are usually 25-45.
4. There are two types of molesters: Situational (often involving a stepchild, relative or girlfriend's child or a child in his/her care (like a preschool worker, teacher, counsellor, boy scout leader, cop or priest/pastor); a child is much more likely to be abused by someone (s)he knows than a stranger) and predatory, which are much more dangerous and at times lead to the kidnapping/rape/murder of the victim.
5. Any crime or moral violation begins with the thought. Although a pedophile (by definition) hasn't committed a crime (yet) (s)he has the mental baggage that could easily allow a molestation to occur.
6. Situational molestation is a violation of trust. Grooming is a term used to describe the choosing and preparation of a child for an act of molestation; most molested children trusted their molester and much of the mental baggage is more a result of the violation of this trust than any sexual act itself (unless penetration is involved, which also includes oral sex.) In many cases the molester is trusted by both the child and the family involved; the disclosure is usually devastating and sometimes met with disbelief and denial, which is further damaging to the victim.

I'll agree with the poster who says a pedophile shouldn't be stigatized for his/her thoughts alone; they should be able to seek professional help and also the support of family and friends. The problem here is that every adult has sexual urges and probably what some would regard as perverted thoughts and actions; such is human sexuality. However few of us regard children as sexual objects, and while our heads might be turned by a pretty little 13 or 14 year old girl who is suddenly becoming a woman, we overrule our sexual instinct with learned judgment and move on. A pedophile doesn't always have that barrier in place; that is the danger.

In regard to the movie, Walter has crossed the line and been punished for it with 12 years in prison. His counselling is shoddy at best; in no way should he be allowed not to disclose what occurred between him and his sister (nor would it be in modern post-prison therapy.) His forays to the mall and park are treading dangerously close to re-molesting. (He also wouldn't be allowed in any state including PA to live across from a school or playground.)