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: Everyone laughs off any reference to the supernatural and the Ghostbusters being any more than hacks. However, they drilled a hole that unveiled a literal river of pink glowing goo that is even brought up at the trial; nobody investigates its origin or acknowledges the fact, which is exceedingly absurd since it involves heavy pollution of the underground system of a metropolis.
Stupidity: The Ghostbusters solve their problem with the evil slime by taking their clothes off; even doing so, they bathed in it, their faces and hair are coated in it and so are their boots. They are carrying with them doses larger than anything previously shown in the movie of a substance a mere smear of brought objects to life, but nah, everything is fine.
Chosen answer: After the initial high of saving the city from Gozer wore off, they were blamed for the danger in the first place and sued out of business. The restraining order was additional insult to injury.
Captain Defenestrator