Stupidity: When the parents knew Freddy was doing the killing then why didn't they watch him like a neighborhood watch so they could catch him trying it again, and thus avoid the legal technicality which threw out of the first case? It seems idiotic they broke the law to punish this lawbreaker.
Suggested correction: The parents believed Freddy would not face justice for his crimes. They were unwilling to allow him the opportunity to kill another child, and believing the justice system had failed them they took the law into their own hands. They completely got away with their vigilante justice. The only bad thing that happened was Freddy was brought back as a vengeful demon with superpowers. There is no way the parents could have known this would happen.
It is still a stupidity. Even if they wanted him to suffer, they would try to avoid legal problems at all costs. It is good that they wanted to prevent him from killing another child but they still shouldn't act so hastily.
Stupidity entries are not meant to be stupid acts by characters. They're for minor plot holes. Without in-film evidence why the acts would be a plot hole, there is no stupidity mistake. And assuming what characters would or would not do does not make a valid mistake (not to mention revenge killings do happen in real life and in movies a lot).
No, it's not. What else were they supposed to do when he was caught and set free? It's still not their fault what happened next.
Stupidity: If the ninja can inhabit a dead body (and one that has been dead for a LONG time, even) without any penalty in his agility and powers and it is stated that only another ninja can truly kill him (which surely seems correct, since he would still fight even when hit by hundreds of bullets), the whole movie plot that involves him possessing Christie - who is a reluctant and part-time host - does not quite make sense.