Continuity mistake: When the three guys who aren't Bill Murray and so don't mind wearing overalls and carrying backpacks pull over as Peter fails to hail a cab, the car's license plate says "ECTO 2", but in the rest of the movie the plate is "ECTO 1A" (apparently because the former would have conflicted with the cartoon, where ECTO 2 was the mini-helicopter). (00:57:45)
Continuity mistake: When Venkman is going to the restaurant and calls a cab, the Ecto-Mobile pulls over and the 3 Ghostbusters exit. The 2 women walking down the street pass behind them twice. (00:57:55)
Continuity mistake: In the abandoned railway station scene, when the heads on stakes appear, you can see in the first shot, Winston is wearing his hardhat after that there is a split-second shot and it disappears. In the very next shot it reappears. (00:59:51)
Plot hole: The Ghostbusters go underground to search for the slime using a map. Even excusing their initial dumb decision to try to dig a hole in the middle of Manhattan when they could have taken that route to begin with, there's no excuse why after their acquittal they never went looking for that river of slime until Vigo burns their lab; they spent weeks studying small samples of the thing but never tried to reach again the source of the infestation to monitor it, which is absurd. (01:00:00)
Suggested correction: The Ghostbusters know from Ray's initial journey down the hole that the river of slime is in the old pneumatic transit system. They are busy re-opening their business and will eventually go back to the river, but that mission gained more urgency once they linked the river to Vigo. Also, they know that the river has been there for years if not decades, and therefore realise that returning to explore it can wait a few weeks.
Continuity mistake: When Winston is run over (or 'through') by the ghost train, he holds the stick at different height between shots. (01:01:05)
Revealing mistake: When Ray, Winston and Egon are underground looking for the river of ooze, there is a scene where they break down a small wall of rocks. Ray then sits on one of the rocks and it bends under him - it's rubber or foam. (01:01:50)
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)
Revealing mistake: When Oscar is standing backwards on the ledge, he moves frame by frame like a robot, revealing it's a stop motion effect and not a real baby. (01:15:00)
Continuity mistake: When the ghost is about to kidnap the baby, Oscar stretches out his right arm. A split second later, from a different angle, the arm is resting by his side. (01:15:45)
Character mistake: At the psychiatric ward, Ray says that Vigo is a XVII century tyrant; it's not a very fitting way to describe him, since he saw the XVII century for just a decade; as the book mentioned, he lived from 1505 to 1610 and was the scourge of Carpathia for the XVI century. (01:16:15)
Suggested correction: Not a mistake, Vigo was a tyrant in the 16th and 17th centuries, Ray chose to label him a 17th century tyrant because that's the century he died in. It would be like calling Osama bin Laden a 21st century terrorist, which is correct, even though he also committed terrorist acts in the 20th century.
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: After Dana rescues the baby in the museum, while she holds him, his head is either turned to the right or to the left, depending on which angle focuses. (01:18:25)
Continuity mistake: When a ghost makes people freak out of the theater, there's a man with a brown scarf who runs towards the camera holding a pop corn bucket. When the angle changes, he's inside the theater, exiting the place again. (01:19:30)
Revealing mistake: People are running away from the movie theater, terrified by the ghosts. Are they really though? The girl at the head of the line (she moves towards the screen from right to left, almost blocking the path of another notable extra that waves around a popcorn bag) just can't keep herself from laughing. Same for a guy that tries to whip the animated fur into submission using his scarf (although one could argue in that case that it's such a weird predicament that a bystander could be amused). (01:19:30)
Suggested correction: Exactly, some people are like the Ghostbusters, they ain't 'fraid a no ghost, which is why they laugh.
Revealing mistake: The second mink in the coat that comes alive is a blatant glove puppet. (01:19:50)
Revealing mistake: During the montage of the ghosts running rampant in NY, one of them in the shape of some sort of dinosaur pops through the archway in Washington Square. It's a ghost solid enough to have to squeeze through the opening and not just disappear through the marble, but when it roars menacingly the optical effect does not work and the superimposed monster does in fact pass through the solid stone. (01:20:10)
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 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: When Ray calls New York "a burned-out burg", a group of firemen behind the Ghostbusters is starting a fight. Cut to Ray in close-up and the fun background activity is no more. (01:25:50)
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)