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.
Continuity mistake: When the guys blast the glass lamp in the hotel, it falls on a table and messes up the table and chairs around. In the following angle the area, which was dark half a second ago is now perfectly lit. (00:35:30)
Continuity mistake: In the first scene the librarian is pushing a cart of books. In one shot both her hands are gripping the back but in the next shot her left hand is holding the top shelf. (00:00:50)
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. (00:44:34)
Continuity mistake: When Ray and Winston are driving back to the Ghostbusters' office, Winston (who is driving) is wearing coveralls; when they arrive and get out of the car, he is wearing just a shirt and trousers. (01:04:00 - 01:08:20)
Continuity mistake: When the Ghostbusters arrive at the skyscraper, a guy with a bulky walkie-talkie appears/disappears between shots. (01:19:25)
Continuity mistake: Louis/Vinz Clortho is dropped at Ghostbusters office at night at the same time Venkman is drugging Dana/Zuul at her apartment. When Venkman calls from her apartment it is night, Janine is in the same grey striped blouse, black skirt and tights outfit during that call she was wearing when Louis was dropped off by the police, at this time Venkman says he is on his way back to the office. Venkman does not arrive until the next morning, during the EPA raid, he is still wearing his same brown date night jacket and blue shirt but it's daylight now and Janine has changed into a new outfit, red blouse, grey vest, grey skirt and red tights and does not look like she slept at the office, Egon has also changed at least his tie and put on a suit jacket.
Continuity mistake: After Dana and Louis break the gargoyles their hair is clean, but when they get to the lower floor their hair has foam in it.
Suggested correction: Very true. It has though been corrected multiple times already, because it's quite easy for them to have got some of the marshmallow muck (or 'foam' as you correctly call it since it's obvious shave foam) on themselves being next to the Ghostbusters who were covered in it. I am not a big fan of "it might have happened offscreen" explanations, but this does seem in line with what is shown.
Continuity mistake: During the earthquake, after the ground swallows the police car, the crowd to the left disappears, only to appear half a second later.
Continuity mistake: When Venkamn picks up slime from the library's drawer, the wood is first partially dry with chunks of slime, but a frame later appears all wet with no slime. (00:09:15)
Continuity mistake: When Dana comes to the station for the first time, Ray is working on Ecto1 and it's primer gray, no light bars or equipment. In one of the following scenes they are eating dinner and cheering to their first customer. Then the alarm sounds for their first call to the Sedgwick hotel and they get in the Ecto1 that is all tuned up, painted with lights and equipment mounted. The events all appear to happen in the same day. It wouldn't be possible to do all that work to Ecto1 in the perceived span of time. (00:21:50)
Suggested correction: The key word is, "appear." Even if there are just a few days between the events, it makes sense for Ecto-1 to look as it does.
Continuity mistake: When Ray first tries the fire pole at the station, he is holding it with his left arm with his right hand on the wrist. When he hits the floor, he is holding the pole with his right arm under his left arm. (00:16:10)
Continuity mistake: When the 'disgusting blob' goes through the wall above the vase of ferns after being attacked by Ray, you can see two small amounts of slime appear on the wall. In the next scene, when the food trolley crashes into the table, there is more slime on the wall than there was in the previous shot. (00:33:15)
Continuity mistake: Venkman meets Dana by a fountain. When he says goodbye to her, first a man with a hat passes behind him and disappears in the next angle; then, in a close-up, Venkman is surrounded by dozens of people who vanish half a second later in the wide angle, where the place appears empty. (00:44:45)
Continuity mistake: When Venkman is doing the tests trying to flirt with the blonde student, when she says that the figure on the card is a star, Venkman is first holding the card with his thumb and two fingers. But from the back angle, four fingers are seen extended. (00:03:20)
Continuity mistake: When Egon tries to prevent Walter Peck from shutting down the protection grid, he has Janine and Vinz (Louis) behind him. You can see that Vinz is raising his right arm, but in the next shot his right arm is now lowered down. (01:06:15)
Continuity mistake: When the Ghostbusters are heading for the building, there's a wide view of New York bathed in a sunset light with a red and blue sky. In further close-up shots, there is a clear sunny light everywhere. (01:15:20)
Suggested correction: Most likely the result of the supernatural clouds forming around the building.
If such were the reason it would be the other way around: it should be dark near the building where the ghost-clouds are, but it's not. Therefore it's a continuity mistake due to the scenes being shot in different days.
Continuity mistake: Trying to escape the demon dog, Tully trips over a chair and bangs against the windows of the restaurant. You can see in the first shot that the maitre d' (the guy with grey hair and stache, wearing black) is looking at him. But in the reverse shot, he's smiling at the patrons at the table, and only a moment later raises his head to check out what the fuss is about. (00:54:35)
