Revealing mistake: During the montage of the Ghostbusters starting the business, there's a shot (the one immediately following the Larry King cameo), where the trio are running down a street. Many people are staring at the camera; it may seem fine since the Ghostbusters are running towards the camera, and they are celebrities so it could be argued that the people are looking at them, not at the camera. Look at the guys to the left though; they are looking past them at the camera and one of them even quickly fixes his hair. (00:40:05)
Revealing mistake: In the montage showing the Ghostbusters' rise to success, the body of the USA Today article has nothing to do at all with them, and in fact it is a copy/paste real life article that talks about Geoffrey Faux, economist. A faux article, the prop guy must have had a laugh with that. (00:39:30)
Continuity mistake: When the hotel manager says he won't pay the 5k, the trap is facing him with the top side. As it cuts to the Ghostbusters faking to just walk back in and release their catch, the trap turned 45°. (00:38:50)
Revealing mistake: When Egon tries to shoot Slimer, the wall is charred on the dark section, but the beam is shown hitting the white stucco, which bears no trace of its passage. (00:36:20)
Revealing mistake: The hotel where the Ghostbusters conduct their first sorta-successful disinfestation is supposed to be called "Sedgewick Hotel." However when the trio enters the hallway, through the window you can see the sign "Biltmore's Cleaners", and to the left "One Bunker Hill." The real hotel in Los Angeles used for the movie shoot is the Millennium Biltmore, which is in the One Bunker Hill area. (00:29:55)
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)
Factual error: When the Archbishop arrives, Lenny greets him with "Your Eminence," which is a greeting for Cardinals. However, the Archbishop is wearing purple, while a Cardinal would wear red, indicating he was not a Cardinal. New York usually has a Cardinal for an Archbishop, anyway, and the production team likely just assumed the greeting without knowing the color rules. The correct greeting for an Archbishop would be "Your Excellency." In this case, either the greeting or the wardrobe was wrong.
Character mistake: Peter tells Egon over the phone that he gave Dana "300 cc of Thorazine." Besides the funny implications the movie ignores on how and why he was in possession of it, Venkman says "cc", but the drug is dosed in mg, so at the very least Venkman misspoke (that'd be 1/3 liters!). The line is not in the shooting script and other sources like the novelization just say that Dana had some valium lying around. (01:02:30)
Continuity mistake: When the possessed Dana asks Peter for the second time "Are you the Keymaster?", Peter comes in; notice that Sigourney Weavers' left hand is still at the top of the doorframe, in the reverse shot it's suddenly down. (00:56:10)
Answer: Ron Jeremy can be seen in the crowd outside the firehouse right after the containment unit is shut off.