Other mistake: Ray obtained a small sample of slime through a very little device, a sphere smaller than his fist. The slime is brought back up in court as "exhibit F" and it is said to come directly from the trunk of their car; the sample is almost 1400 ml, way larger than it should be. (00:25:20 - 00:29:05)
Other mistake: When the Ghostbusters are inside Lady Liberty, you can see from their close-ups and from shots inside the head that the windows that form the crown are narrower than their shoulders. Despite that, they easily make the drop on the villains from there, while carrying huge backpacks (the slime ones have large tanks even). (01:30:20)
Other mistake: The Ghostbusters can get inside the museum when the Statue of Liberty breaks the museum's ceiling light. Good, but the whole museum was surrounded by a shell of slime that extended above it too. The Ghostbusters do nothing to open a hole in the slime, nor they could know it would open, and the Statue has nothing to do with it. (01:31:45)
Other mistake: In the Italian dub, the kids at the birthday party vociferously ask for their hero; Tree Man instead of the original He-Man. He-Man was very popular in Italy too at the time, it was not an obscure reference that needed any adaptation - not that there is or was any character named Tree or Tri Man in Italian pop culture.
Other mistake: Dana leaves her home in such a hurry that she does not even put anything on her baby in the middle of December. She shows up at Peter's home, he phones Ray who then rushes out of the door saying he's gonna check Dana's apartment. Peter tells Dana that Ray is going to check her apartment, but their phone convo ended way before Ray had taken that decision, and he has no contact with the others till morning when they meet at the museum.
Other mistake: The whole plan of the Ghostbusters relies on the fact that the Statue of Liberty, being the symbol that it is, will rally the population of New York drawing their positive energies out. Forgetting the fact that a giant statue trampling things in the middle of the city is quite likely to inspire negativity, let's go with the movie's theory; it's not what it is shown. The people start singing, disturbing Vigo, at a random moment that has nothing to do with the statue showing up and in fact happens when it is already just lying on the ground.