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 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.
Stupidity: Dana is really worried about her baby throughout the whole movie. She was literally almost eaten by a bathtub of slime less than 24 hours before. So naturally, when the guys show up to investigate, she blows them off to go on a date. "Women, huh?" (00:58:30)
Suggested correction: Dana asked Janine if she could babysit Oscar for her while she was on her date and Janine said yes.
That's not the point; they are going to check the "slime stuff" (as Peter says) that happens to be the same slime that nearly ate her baby and the reason why she's there and needs a babysitter to begin with, but to her the date with Peter is more important. Like, way more important, she does not even think about it a second.
Peter sees that Dana is stressed out, so he offers to take her to dinner to help ease her. She's reluctant at first until Peter mentions having Janine as a babysitter. After that Dana agrees to use Janine as a babysitter for Oscar as she works for the Ghostbusters and Dana knows how reliable Janine is.
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, and they are sentenced to a fine for a total of $75,000, which is ridiculously low.
Suggested correction: To be fair, their $75,000 fine is equivalent to over $165,000 now after inflation, which seems pretty reasonable to me. (Current law is that fines can go up to $250,000 for damage to government property.) They were also sentenced to 18 months each in prison, so it's not like they were just fined.
I am no lawyer and I may amend that last part where I called the amount 'ridiculously low' since you make a case for its appropriateness (although that kind of damage in that sort of area would most likely deserve the highest possible amount), however the main point is that at the trial they mention the 'stuff down there' that nobody acknowledges for the rest of the movie, and it doesn't even seem to have a bearing in it like its something trivial.
I actually happened to stumble onto a Legal Eagle YouTube video (he's a lawyer that analyzes legal scenes in movies/TV) about the courtroom scene, so I came back to this. (Going through a "Ghostbusters" kick now that the new one is out on Blu-Ray, so I've been watching tons of stuff related to the franchise.) Weirdly enough, he was actually initially surprised by the punishment they got. (Particularly the jail time on top of the fine.) Although he admitted that it just depends on the charges given they also knocked out power. I think most of your mistake stands fine as-is (it is a stretch at best that the authorities wouldn't investigate it further, and most likely constitutes a genuine plot-hole), but I'd personally remove the last bit about the fine, since if anything, that's probably a pretty accurate fine judging by Legal Eagle's reaction.
