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. (01:35:50)
Continuity mistake: When the heros arrive at Dana's building, they're saluted by a crowd. If you pay close attention, you'll see the same extra in two different positions (he's the young - and very "happy" - guy wearing a grey suit and a purple tie). (01:19:30)
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. (00:38:50)
Revealing mistake: When the Stay-Puft Marshmallow Man is walking through the city, in several shots you can see outlines of people and buildings through the marshmallow man, who was added in optically. (01:32:05)
Continuity mistake: As the earthquake happens and the ghostbusters fall in the crack, the close-up shot shows Ray holding his gloves, yet in the immediate cut away he is wearing them. (01:20:30)
Continuity mistake: When Dana returns to her apartment (the first time we see her do so) she is carrying a bag of groceries. The contents at the top of the grocery bag change with each shot: one time celery, then bread, then eggs, etc. (00:17:00)
Continuity mistake: The large blue book that Peter drops on the table to startle Egon disappears off the table in the next shot. (00:07:10)
Revealing mistake: During the "montage" there is a reversed shot of the guys driving their "ghost-mobile" - you can notice it because the Ghostbusters logo is reversed. (00:39:35)
Visible crew/equipment: Bill Murray and Dan Aykroyd's stunt doubles are visible in the shot (from behind) that shows the Ghostbusters falling into a hole. (01:20:35)
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. (00:16:50)
Continuity mistake: When the demon breaks out of the statue on Dana's apartment building, it breaks away the right paw. When we see the statue after the demon is out, both paws are intact. (00:48:55 - 00:51:55)
Continuity mistake: At the hotel, when the Ghostbusters blast the cleaning lady's trolley, the stuff on the floor changes between shots. Watch the toilet paper on the far left, for example. (00:31:50)
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. (00:22:10)
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)
Revealing mistake: When the ghosts are released from the storage unit, there's a shot of the light beam followed by a wide panoramic view of New York where the ghost lights depart as strings and orbs of energy. If you look at the Empire State Building, you can see that the first orb supposedly passes behind it, but its outline can be in fact seen through it. (01:09:05)
Continuity mistake: When the mayor orders Walter Peck out of his office, you can see that he is pointing his finger at Peck, but when the camera angle changes his hand is nowhere to be seen. (01:17:45)
Continuity mistake: When we see Dana for the first time, there is an aerial shot of her taxi pulling over to drop her off. The front end of the taxi drives into the view of a tree, however when Dana gets out of the cab, the tree has vanished and there is a clear view. (00:16:50)
Continuity mistake: In the scene where the earthquake begins, the Ghostbusters fall into a hole. They're in two rows - in the first row are Venkman and Ray and in the second row are Egon and Winston. In the following shot, it is now Ray and Winston on the first row and Venkman and Egon on the back row. (01:20:30)
Continuity mistake: When Stay Puft is walking towards the church, an aerial shot shows the (miniature scale model) streets totally empty; however, a floor-level angle shows hundreds of (green screened) people who have appeared from nowhere. (01:32:05)
Continuity mistake: When they're all fighting in the Mayor's office, the mug on the desk changes its position between shots.
Answer: Ron Jeremy can be seen in the crowd outside the firehouse right after the containment unit is shut off.