Criminal background checks while necessary for certain jobs are not the be-all, end-all that some would like to think they are. It is important to understand the limitations of such instruments.
Quite frequently a story will appear in the news about someone who has violated the public trust by allegedly committing a criminal act. One of the first questions that is always asked is if a background check was performed, and did it yield anything that should have be flagged as suspicious. It is important to understand that a criminal background or history check is just that, an inquiry as to if the individual in question has a prior criminal record. It is not a physiological assessment of the person nor is it designed to attempt to predict future behavior.
That fact is necessary to understand, as it is important to realize that every criminal had a first crime. Somewhere out there is a first victim, or at least the first time the individual was caught and convicted of committing a crime. If the person in question never exhibited this behavior before, or was never caught, a background check is going to be negative.
The person in question may be very good at hiding their tracks as well, especially if they are bullying or harassing someone. They may know just how far to push someone before they are reported, and they may also leave the situation where the incident(s) are occurring. The victim in this instance may have just wanted the offensive behavior to stop, and by the perpetrator leaving, that solved the immediate problem. The victim may feel that the only outcome of a complaint would have been the termination of the offender, and now that they have left of their own volition, there is nothing more that needs to be done. There is no need to get "tagged" as a person who makes waves.
Predicting who may or may not be an offender takes much more than a background check, that's profiling, and the profile generated may not necessarily reflect what the individual is capable of doing. If you examine serial killers for example, you will see that many of them are not social misfits, they have families and are gainfully employed; basically they fit in and are not obvious in any way. (Source FBI) Predicting criminal behavior is not easy as the movie Minority Report demonstrated. It gave us a glimpse into a future where crime could be predicted, but it also showed how such a system can be flawed and manipulated.
Unfortunately there will always be predators out there, and there is not one catchall for identifying them. Watching their behavior will not always indicate a potential problem, but watching the reactions of those around them might help. A victim may be a willing participant at first as they may see nothing wrong with the behavior exhibited by the perpetrator; also it is not uncommon for the predator to make the victim feel that what they are doing is right, but needs to be kept secret. Anything that you need to keep secret is something that you might want to question as to why. Adults have a better understanding of what should be kept private, but children should always consult their parents if someone asks them to keep a secret, especially if that person is another adult.