Continuity mistake: At about the middle of the film, when the Ghostbusters are rising to fame and are appearing on the front of newspapers and magazines, the photograph on the front of the New York Post is taken from the end of the film, just before the four of them cross the streams from their proton packs.
Revealing mistake: In the ballroom scene, when Slimer is flying around the chandelier, he disappears for a few frames when he reaches the far side. [This animation is mentioned in the DVD commentary. The film makers were generally unhappy with the entire animation and the fact that the representation of the apparition did not resemble those previous and that the movement was very unconvincing.]
Revealing mistake: Near the end of the film when the Ghostbusters take cover in a small corner and come up with the "cross the streams" plan, look closely at Peter's proton pack, you can see that it is a foam "stunt" pack as there is a small sticking out part that keeps squashing against the wall behind him.
Continuity mistake: When Winston gets hired, Venkman and Stantz have just come back from a job. They're covered in slime and Venkman's smoking. Ray gives Winston an armful of traps. We then cut to Venkman chatting to Dana after a rehearsal, so we assume it's later, maybe even a different day. After that scene though, we then cut back to Stantz showing Winston (wearing the same shirt) what to do with the traps, and Venkman talking to the guy from the EPA. Venkman's got the same slime pattern on his shoulder, and is still smoking. Looks like the Dana/Venkman scene was in the wrong place.
Plot hole: The Ghostbusters cross their proton pack streams which results in a tremendous explosion. The next scene shows the blast pushing Mr. Sta-Puft away from the building. A second later another scene shows the explosion radiating outward from the roof. The only part of him shown over the edge of the building is his head and his right hand. To get all over the Ghostbusters, marshmallow would have to be blown in the opposite direction against the force of the blast. It makes sense that there was marshmallow all over the street, but how did it land on the Ghostbusters?
Add timeGrumpy Scot
Revealing mistake: The first time the heroes use their proton weapons (in the hotel sequence), you can see (using slow-motion) that the rays don't actually come of the weapon, but from their target. The rays were "drawn" during post-production and, apparently, it's easier to start drawing from the target to the weapon. (According to MM rules the use of slow motion IS permitted for viewing something significant, such as a 'revealing' mistake.)
Continuity mistake: In the scene when they are emerging after the Stay-Puft explosion, we see Ray with marshmallow on his face and a small amount on his chest. He wipes his face, but in the shot following his apology for the burnt dog hair comment, his front side is completely covered in the stuff.
Continuity mistake: When the hotel manager refuses to pay the bill after the Ghostbusters capture the green ghost (Slimer), you can see he is putting his handkerchief into his top pocket with his left hand, but in the very next shot he can be seen putting the handkerchief in the pocket with both hands.