Continuity mistake: When Ray passes the paper with Vigo's biography to Peter outside the museum, the passers-by change at the cut. (00:50:00)
Continuity mistake: Peter leaps on his own bed after telling Dana that she can treat his house as her own. Between shots, the spare clothes tucked under the covers and those lying on the box by the window change entirely. (00:48:45)
Audio problem: Dana shows up at Peter's door with poor little Oscar desperately crying after the bathtub misadventures. Is he really crying though? Sigourney Weaver does her best to hold the baby close to her and away from the camera, that shoots the scene cutting off above the mouth level. His body language is composed though, and for one moment (when Dana says "this pink goo everywhere" his mouth pops in frame and it is closed. (00:46:20)
Continuity mistake: When Dana tells Peter that she thinks the painting is watching her, Peter turns towards Vigo with the whole body. In the close-up, he's glancing at the painting sideways facing Sigourney Weaver. (00:44:25)
Continuity mistake: Peter drops by the museum to see Dana. As he enters room 304, a worker there is wheeling away a big crate. Cut, and the crate spun 90° (just check the stickers and the "Keep dry" writing, first on the right side, then on the side facing the worker). (00:42:40)
Revealing mistake: In the courtroom scene, when the sample of slime begins to bubble and react to the judge's malevolence you can plainly see that an inflatable mechanism situated under the jar is responsible for the wobbling. (00:32:00)
Continuity mistake: The prosecutor interrupts Tully being fed every line saying that he's "leading the witness." She leans on the table, but before the cut ("Mr Tully...") you see her pull back and begin to raise her hands. Next shot and she is still palms flat on the table. (00:30:25)
Continuity mistake: After they trap the Scoleri Brothers, Spengler lifts his foot from the trap mechanism. In the immediate angle his foot is still on it, and he is lifting it again.
Continuity mistake: Before the trial, Tully leans over the table and tells the boys that he got his law degree at night school; Ray in the reverse shot is holding his pencil at table level, while it was well under it out of frame in the previous. (00:28:00)
Revealing mistake: When Ray kicks and breaks the pipe in the underground, the prop was obviously put together to break at the flimsiest touch; it's not just a corroded or even cracked pipe, the two parts are not even of the same color, they were never a single piece to begin with. (00:25:40)
Continuity mistake: In front of the puppy testing box, Egon tells Dana not to worry and lowers his instrument. Dana gives him her number in the next shot, which begins with Egon holding the device higher again. (00:07:15)
Continuity mistake: When the prosecuting attorney walks up to the witness stand with Peter on it, she stands off to the side. When Peter puts his hand on hers in the next shot, she's standing in front of it. (00:31:25)
Continuity mistake: When Lady Liberty shows up on the streets, she makes a left turn towards a big avenue. From the ground shot the police cars and motorcycles have moved ahead and the road is clear. From the aerial angle the cars and motorcycles are right next to the statue's feet. (01:29:35)
Revealing mistake: In the aerial angle of the Statue of Liberty walking down the streets, watch behind it: it is very evident where the matte painting was inserted: The street colour differs and the objects have way less definition.
Revealing mistake: When Lady Liberty walks down the street, the four Ghostbusters inside its crown are replaced with very obvious dolls. (01:30:05)
Continuity mistake: When Louis is saying 'his place at 8' there is a guy in the background on the right hand side on the sidewalk. When it cuts to the long shot and he is almost hit by the taxi, the guy is gone. (00:56:00)
Other mistake: When the Ghostbusters are inside Lady Liberty, you can see from their close-ups and from shots inside the head that the windows that form the crown are narrower than their shoulders. Despite that, they easily make the drop on the villains from there, while carrying huge backpacks (the slime ones have large tanks even). (01:30:20)
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 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)
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.