Continuity mistake: Dana is at the Ghostbusters' who just tested her with a device. When she says that she does not believe in 'those things', Ego picked up a cheez-it and brings it to his mouth. In the next shot he's not the one with a snack to his mouth, Ray is. (00:23:25)
Continuity mistake: The guys have just been thrown off campus. A liquored-up Peter walks Ray to the right explaining; "I believe that everything happens for a reason." Before the camera cuts away, you can see the head of a girl with a red ribbon in her hair that is going down the stairs. Next shot and she hasn't even set foot on the first step yet. (00:14:45)
Continuity mistake: The future Ghostbusters don't have a clue yet what to do with the ghost of the librarian. They send Peter first, who tries to work his charm saying "Hello. I am Peter." Harold Ramis in the background is pointing the camera at a different height/angle between the two shots. (00:11:30)
Continuity mistake: Venkman is questioning the shocked librarian about possible use of drugs. Director Delacorte in the background is half turned towards them, but he's facing them directly in the close-up when Venkman says "Just asking." (00:08:05)
Continuity mistake: The shot that introduces the existence of the Ghostbusters is a shot of the door of the "Paranormal Studies" laboratory inside Columbia university. It's a door that opens to the left and bears a glass panel with the names of the 3 scientists. When the shocked kid and Ray use it though, the door swings the opposite way. And when the Ghostbusters get back to their lab and find the Dean there, it's a double door with no glass, which was a prop built just for that opening shot. (00:02:45 - 00:13:10)
Continuity mistake: When Slimer flies off after Ray shot towards him the first time, the cart rolls away; you can see that the champagne bucket was not knocked down by the messy explosion. When the cart crashes in the wall, the bucket enters the frame already lying horizontally. (00:33:10)
Revealing mistake: When Ray shoots at Slimer, the proton beam reaches the door in the first shot, and in the next one goes past it; its future path inside the wall is already outlined and burnt to a crisp. (00:33:10)
Continuity mistake: When Peter sets foot into Dana's house, in the establishing shot of the room you can see two pink pillows on the armchair. Between their first and second appearance the pinker one in front has slumped. (00:24:15)
Continuity mistake: Egon is done testing Dana with the electrodes on her temples. He walks past her pronouncing a line; " I wouldn't rule out clarvoyance." There's a cut during the sentence, and in the first shot Dana is looking up at him, in the second she is looking at the floor. (00:23:20)
Revealing mistake: In the very first indirect manifestation of the ghosts (the floating books), you can see on top of the stacks the rigs that allowed the strings to pull the books across [Noticed by Ivan Reitman during the DVD commentary]. (00:01:15)
Continuity mistake: The librarian is carting away books that are (for the greater length of the top shelf at least) leaning away from her. Cut, and they are positioned differently, about one third towards, a part in the middle away, and again towards her. (00:00:50)
Revealing mistake: The Ghostbusters' containment unit explodes with a sinister beam that blasts through the rooftop. In the shot with the camera at street level showing New Yorkers running scared, you can see a blatant light 'halo' around one of them as by-product from the optical effect. (01:08:00)
Continuity mistake: When Dr. Venkman investigates Dana's refrigerator, there is a Corning dish and a can of Coke side-by-side on the top shelf. The camera cuts twice, and there is suddenly another item (looks like lunch meat) that appears in front of the Corning dish and the Coke can.
Continuity mistake: When the Ghostbusters capture the green ghost, they emerge from the ballroom. The manager then asks,"Did you see it? What is it?" and you can see he has his hands by his side, but the next shot shows him with his left hand reaching for the handkerchief in his top pocket.
Continuity mistake: During the party, when Louis throws the coats on the gargoyle's head, its horns are visible from the front shot, but covered in the immediate angle from behind. (00:53:20)
Continuity mistake: When the eggs are flying in Dana's kitchen, she approaches the counter and comes inches away from it, yet from a wider angle she is several meters away. (00:19:20)
Continuity mistake: When Peter arrives at the library, the blue book he later slams is on the far left of the table. A frame later it's on the far right. (00:07:00)
Continuity mistake: Stay Puft walks behind a church, which appears or disappears depending on the angle.
Continuity mistake: When the movie is about to end, the Ghostbusters are in front of the building and the pavement starts to crack open. A group of men by the door stumble off-screen to the left. Half a second later, a close-up shows the people repeating all the previous movements.
Continuity mistake: When Venkman walks down to the library's basement, his tie changes from skewed to straight. (00:08:35)
Answer: Ron Jeremy can be seen in the crowd outside the firehouse right after the containment unit is shut off.