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)
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)
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)
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)
Continuity mistake: Dana gets home and puts down on the table the paper bag with food and her coat as she answers the phone. She takes her shoes and pants off and the camera cuts away to a different angle where the coat and the paper bag have changed position. (00:51:00)
Continuity mistake: Dana witnesses the horrific appearance of Zool inside the fridge, and as she tells the Ghostbusters, slammed the refrigerator door shut and left. However, when Peter talks to her in the living room after he checked the fridge himself, you can see that the items on the table (the one by the TV she watched the commercial from) have been radically rearranged, something she surely wouldn't do leaving in a hurry. (00:19:00 - 00:26:55)
Continuity mistake: The silly bureaucrats cut power to the containment grid, which is about to blow up. Everyone runs away from the building; there are two main camera angles on the exterior, but they are obviously not in continuity - in the closer angle, natural light shines on the street to the right, while in the wider/higher angle that side of the building is in the shade. (01:07:50)

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. (00:53:25)

Continuity mistake: When Dana opens the door of her refrigerator and sees the temple with a terror dog, the shelf has a bottle with a green cap and a jar with a white lid at the end of it, but when Dana slams the refrigerator after the dog says "Zuul!", both items have disappeared. (00:20:00)
Continuity mistake: When the road cracks and swallows the police car, the distance between the ambulance behind increases and decreases between shots.
Continuity mistake: When the Stay Puft monster appears and all the cars crash, a driver goes out of a grey car through the window. In a closer angle he is back inside and repeating the movement. (01:31:15)
Continuity mistake: After the pavement cracks and swallows a police car, the chunks of broken pavement next to the car differ between shots. From a back view there are smaller pieces, but from a front view they are a couple of big and long chunks. (01:21:00)
Continuity mistake: When the Ghostbusters run out of the library, an old woman in a blue coat is seen on the left side by the bottom of the steps. A second later she is all the way up and coming from the right side instead. (00:12:20)
Answer: He places it on the altar just after they believe they have vaporized Gozer with the proton packs. At this point, thinking the ghost to have been destroyed, he sets it down as he believes the job is done and he will not need it.
Jazetopher