Stupidity: Lao Che's intention was to kill Indy. He had no intention of giving him the antidote. So then why would he bring a real antidote? Why not just fill it with something else instead? From his perspective, bringing a real antidote was a waste of time, and also very stupid in case Indy managed to get it, which he did. In fact, Lao Che could've brought a fake antidote and given it to Indy. He probably wouldn't have noticed the difference, and then there wouldn't have been a fight in which one of his men was killed.
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.
Stupidity: It's mostly a fun absurdity, but it is somewhat contradictory to showcase the Ghostbusters being featured as the cover story of every major publication and news outlet, and yet to get help not only they put an ad on the newspaper, but a single person applies for the job (which is all it took for them to accept).
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.