Stupidity: Monk steals the magazine from Coffey's SIG. However, I don't see how he could have jacked the slide to eject the round in the chamber without being noticed. Someone as paranoid as Coffey was at this point would not have left the chamber empty. (Just FYI, when you load an automatic pistol with a magazine, you have to pull back and release the slide to load the first bullet in the barrel.)
Stupidity: Suspension of disbelief is fine for a movie like this, but even as a child I found unbelievably silly the fact that the Ghostbusters use a Nintendo controller to move the Statue of Liberty. The concept is never set up and never is shown properly; all the movie showed and told us was that items possessed by the slime dance wildly to the beat of music. There's no logical (as in, movie internal logic) passage between that and "so we fire up some beats and it won't start dancing to it, but just calmly move according to our inputs on a joystick."
Stupidity: The murder during the opening scene is ridiculous. Angela chases a screaming woman down an alleyway, in broad daylight, in front of crowds of witnesses, while driving a truck, runs her over, then throws her body in the back of the truck and then waits right next to the alley where she murdered the girl to be picked up by the van headed to the camp. At no point did any one of the numerous people on the street try to help the girl or even just investigate the alley to see if she was hurt (supposing it was an accident) or just call the police?
Stupidity: At the start of the tanker chase Sanchez shoots at Bond. He manages to get in the cab and throw the driver out, who lands on Sanchez's car. Sanchez then gets in front of Bond and has the ideal opportunity to just shoot the cab up with his machine gun knowing Bond is driving, but he doesn't.