Other mistake: After the guys decide to rent the building, the shot of New York from the park is the very same one, though with different sky colour, to that of the moment when they are about to battle Gozer. Though it's a very wide and common shot of the park, the very same people are laying on the grass in the very same position in both shots (big screen recommended to spot it). (00:16:45 - 01:18:35)
Other mistake: Winston Zeddemore's surname is spelled as "Zeddmore" in the closing credits. (01:43:50)
Other mistake: How could Egon get down to the ground floor so quickly? I mean, a few moments earlier, he poked a guest in the shoulder. And, why would he go back down to the first floor in the first place? They said that nothing happened on any floor except the twelfth.
Suggested correction: Egon probably was able to track Slimer to the ballroom immediately after he slimed Venkman, Egon never says he was on the first floor, he probably knew the layout of the hotel and picked up Slimer's trail heading for the ballroom.
But Egon says, "get down here right away, it just went into a ballroom." That line alone indicates he is already down there.
Egon can still say 'get down here right away" while he himself is still en route to the ballroom.
Somehow I don't believe a man as intelligent as Egon would use an improper term such as "get down here" unless he was already at that location. He more than likely would have said, "get down to" or "get down stairs." Speculation yes, but in terms of his character, I feel this makes sense.
Other mistake: After the trio stormed off the library, they are walking around the campus. As Venkman giggles mocking the "Get her" lack-of-a-plan, to the right of the screen there's an elderly lady who keeps staring curiously right at the camera. (00:12:20)
Other mistake: As Gozer is flipping over the Ghostbusters, we can see some sort of ceiling decoration, but they are on top of a building and even the open portal door shows no roof above them.
Suggested correction: That's actually part of the building spire with clouds above it. Not a ceiling. The clouds are fake of course and not moving so it looks like a ceiling. You can see this spire again when he marshmallow man is fired upon by the ghostbusters and the explosion later.