For example say there is a pedophile who was not convicted (or even taken to court). First you have to ask yourself why he wasn't convicted. If there was a lack of evidence then how can you be so sure that the person is a pedophile? Or how can you fault a jury's ruling if there really is a lack of evidence? Perhaps the injustice is only imagined in your head. That would be the first thing to consider.
But maybe it's not that simple. Perhaps the pedophile is an influencial bishop or Micheal Jackson or something, and they weren't convicted because of their wealth and status. Well you can bet that whenever there is corruption you won't be the only one to notice. You can look for allies, because there will be others upset about the injustice. Then together you can seek legal means of retribution. The Catholic church is dealing with gigantic monetary damages right now, because of lost pedophilia lawsuits. Also retribution might be something as simple as letting everyone in the area know that so and so is a pedophile. Damaging the person's reputation can be quite effective and doesn't risk the consequences of murder as retribution.
Ok, but say none of that really applies in this situation, and that child molesting motherf****r really just needs to be shot. Well don't count the legal system out entirely. I don't hear this mentioned often, but jurors are actually law makers to a certain extent. The scope of their authority is extremely narrow but potent. They can decide what the law is for the one specific trial in question (and also influence similar trials in the future). So a jury might decide that the lawmakers didn't think of this specific case, or they might just decide that the lawmakers are pompous idiots. Either way the final say in legal matters lies with the jury and not the legislators.
There have been cases, for example, where a jury has given a lesser sentence or no sentence to a wife who has killed her husband because he was abusing his wife. Technically murder is illegal, but in that spefic case the jury made it legal. Another thing to remember is that in our legal system, all things being equal, a person is more inclined to be not guilty than guilty. In other words guilt needs to be proved, but innocence does not. So while a jury might not convict a pedophile on lack of evidence, they might not convict the person who killed the pedophile either (or at least give a lesser sentence).
Well what if none of that works? Then you are going to jail. Serves you right for taking the law into your own hands.