Continuity mistake: There's a scene where Spengler talking to Ray about Iran running Vigo The Carpathian through the Occult Reference Net. We first see the computer screen from the side, with Spengler and Ray looking at it, and in the next screen we see the screen head on. The layout of text on the screen, the books piled to the right and the shadow on the wall to the left are all different between scenes. The close-up of the screen is obviously a different set-up, close but not right.
Continuity mistake: During Oscar's physical, Ray is holding the recorder in his right hand, then as the camera switches to the reverse angle his tape recorder is in the left hand. (00:16:50)
Continuity mistake: Ray answers the phone getting a momentary break from Peter's questioning. He picks up the receiver holding a pencil between index and middle finger, but when the camera angle changes the pencil is gone, and he later picks it from the book on the desk. (00:14:35)
Continuity mistake: When Janusz is knocked off the ladders while painting Vigo's eye and Vigo comes to life in the painting, the brush he was using is in different positions on the floor depending on the shot. (00:22:30 - 00:23:05)
Other mistake: In the Italian dub, Egon mentions that he raised the room temperature to 42°, which would be almost 108 F, instead of the correct 95.
Other mistake: In the Italian dub, the kids at the birthday party vociferously ask for their hero; Tree Man instead of the original He-Man. He-Man was very popular in Italy too at the time, it was not an obscure reference that needed any adaptation - not that there is or was any character named Tree or Tri Man in Italian pop culture.
Continuity mistake: The Ghostbusters pick up the 'symbol' for their fight by looking at the license plate of their Ecto 1A, which sports in close-up the Statue of Liberty right between the O and the 1. Problem is, in the rest of the movie, and that includes just a few shots before when they were blasting the jelly shell with their protons, Lady Liberty is to the left of the plate, before the E. (01:26:15)
Continuity mistake: When Hardenmeyer is escorted away from the room, the Mayor points his finger at a staffer and tells them to get the Ghostbusters. Another staff member calls his attention, but in that shot we see David Margulies through the window, and he is in a completely different position. (01:22:10)
Continuity mistake: When Peter tells Ray to hose Lucasz, Dan Aykroyd's hand is below and then above the slime gun in the two separate shots. (01:32:15)
Continuity mistake: When the Ghostbusters approach the giant uterine slime cocoon to try to breach into the museum, there's a group of firemen to the right. The late arrival to this group brings an axe. Cut to a wide shot and the guy is not carrying the axe anymore. (01:24:05)
Continuity mistake: Janosz is kinda bored as he awaits for the word of Vigo, the scourge of Carpathia. In close-up as he hears "I, Vigo..." he grimaces with his hands at chest height and not any wider than the shoulders. Turning to the wide shot, he is listening with his hands raised and the arms spread. (01:12:25)
Continuity mistake: When Dana tries to take Oscar back from the museum on her own, the cloth on top of the pillow where Oscar is resting goes from crumpled to straight. (01:18:20)
Continuity mistake: Tully is chasing Janine after she wished him goodnight. When the camera cuts closer to them, the cars parked on the sidewalk change abruptly, and they get back to the same models only at the end of the scene when someone honks a horn at him and the camera switches back to the original angle. (00:55:35)
Continuity mistake: While Peter is doing his pantomime with Vigo's painting saying "Walk for me talk for me, yeah!" you can see Dan Aykroyd stiffening on the ladder, acting as if Ray suddenly got possessed/mesmerized by Vigo. In the close-up that follows we see the process happening in a different and more gradual way. (00:51:40)
Continuity mistake: Janosz interrupts Dana and Peter talking about the Gaugain; behind him there are a man and an elderly lady passing by. Cut to Sigourney Weaver, and in the next shot the two people practically haven't moved. (00:43:10)
Continuity mistake: When Ray screams at the slime that "YooOOOuuUUU take the cake" his wrists in the background are crossed and the watch is visible. Cut, and his hands are joined and the wristwatch concealed. (00:39:45)
Continuity mistake: When Peter crawling like a worm draws the attention of the scourge of Carpathia that is holding the baby, shouting "Not so fast, Vigo!", notice Vigo's hair moving from the back of the right shoulder to the front. The hair changes position going in front of both shoulders to various° in the rest of the conversation. (01:34:55)
Visible crew/equipment: Vigo just knocked down the heroes who are looking at him powerless. Vigo then makes a gesture and parts the crates behind which Peter hid Oscar. As he does that gesture you can spot in the background on the left (mostly in the darkness) someone's arm doing the same (the movement is not exactly the same so it's not a mirror). (01:34:35)
Revealing mistake: When Vigo repels the Ghostbusters after they shot him, the lads bounce against the background...that bounces back against them, despite being 'solid concrete'. (01:34:10)
Continuity mistake: When Egon sucks the Scoleris inside the trap, the three 'busters are spread across the courtroom, but in the close-up of the trap you see their legs being much closer - and you can see for instance by Peter's stance that there's no real continuity. (00:36:20)
Chosen answer: After the initial high of saving the city from Gozer wore off, they were blamed for the danger in the first place and sued out of business. The restraining order was additional insult to injury.
Captain Defenestrator