Stupidity: When Johnny is captured by Roarke and his followers, Danny gives him the power of the Ghost Rider back. Roarke knows what Danny is doing, but doesn't order his men to stop him, or even attempt to stop Danny himself.
Stupidity: Jill wasn't thinking too clearly when she plans her story. She only wiped the fingerprints off the gun but they would be all over the tape on Trevor's body. Then she wipes off the knife yet touches it again to slide it across the floor. She was thinking that Trevor and Charlie were going to be thought of as the killers but their fingerprints weren't on either of the weapons.
Stupidity: All the mutants on the island need Magneto at the last second to take control of the missiles so they don't land and explode. Why didn't Azazel just teleport everyone off the island?
Suggested correction: Given the situation, there was probably very little time to come up with a plan like this. The missiles were flying towards them extremely quickly, and there would have been nowhere near enough time to band every single person together for Azazel to teleport them all out of there in just a few seconds.
There was plenty of time. He could have taken 5 at a time down the Beach 3 miles and came back for the rest. Earlier in the movie he was moving so fast men were falling from the sky at nearly the same time and he was teleporting them one at a time.
Stupidity: The protagonist has a sophisticated alarm system with cameras...that do not properly show who is at the gates (the cameras are positioned in a way that does not show the face of the person ringing). The bad guys are disguised as police officers...and wear ski masks, which would have made the disguise entirely pointless - but luckily for them, Nicholas Cage can't operate cameras nor looked at the ones on the entryway or the front of the house, didn't open the door sooner nor peeps before opening. They could not know any of that, though, just that the camera at the entrance has a terrible angle.
Stupidity: Spoiler alert. After the son makes it out, he could get a rescue team to get his dad by going in where he came out.
Stupidity: There is a scene about a null hypothesis proving Cassius is the killer. Nearly everything is wrong in this scene. Statistically, you never prove a null hypothesis true. (01:23:11 - 01:24:22)