Revealing mistake: A shot from above Dana Barret's apartment, from just above a statue looking down on the road below: The statue in the foreground is partially transparent. We can see the double yellow line on the street go straight through one of the statue's upper fangs, and one of the white lane dividers going through the statue's lower jaw. Viewed on Bluray disc.
Continuity mistake: At one point in the movie we see the end of the hallway in Dana's apartment and the end is of a window and the wall around it is red like the end near Dana's door. However, (either when the Ghostbusters arrive at the end or when Louis is being attacked by the terror-hound) the whole hallway (even the other end) is all white.
Visible crew/equipment: When Dana arrives at the Ghostbusters' office, a crew member can be seen moving behind the filing cabinets behind where Janine is sitting. It could be Venkman, but even after Venkman walks over to Dana, there's still a rogue hand there, showing us it wasn't Venkman and was a crew member.
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.)
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.]
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.
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.
Continuity mistake: At the Lincoln Center (that place Dana's orchestra plays at) the nerd with her has his case and they're leaving when Peter is there. Nerd-boy goes off to the side and waits. When they start off again, his case pops back and forth unhumanly between being carried under his arm and in his hand between long and close shots about 3 times.
Continuity mistake: After Louis asks if anybody wants to play Parcheesi at his party, there is a lady sporting a red vest behind him, standing in front of a wall with framed photos. Two shots later, she's standing in front of the kitchen next to a bespectacled man. The very next shot, she's teleported back to where she was initially, in front of the wall.