Audio problem: During the fight with the Scoleri Brothers, Egon warns doctor Stantz about the sudden apparition of the ghost coming through the wall. He yells "Behind you, Raaay!", but in the close-up Harold Ramis' mouth is not uttering "Behind you." (00:35:50)
Continuity mistake: After "Do, Re, Egon", the Ghostbusters are nervously waiting for the Scoleri to show up, as if they knew they would. Just before the camera cuts to a close-up on Bill Murray, he begins to lower his head to look at his rifle, but in the close-up he is facing forward. (00:34:40)
Continuity mistake: The smaller Scoleri tosses the defense table at the judge's empty podium. In that sequence there are no burning fires (a tiny one quickly fades) and not even the glowing jar of slime. When the Ghostbusters arm up, the slime is smoking and glowing and fires burn at the judicial bench. (00:33:05)
Continuity mistake: When the Scoleri Brothers come (for whatever reason) out of the jar there are strong air currents all over the courtroom. The heroes are under the table, and you can see the winds knock down a few books above them. In the reaction shot on the crowd after Ray goes "Wooooow", you can see some of those books that just fell earlier still on the table. Look for instance at the two books by the red tome to the far left. (00:32:40)
Continuity mistake: The boys upstairs hear Ray screaming to pull him back up from the hole in the ground. Venkman is leaning against it with his left hand, which turns into the right hand at the first cut. (00:25:30)
Continuity mistake: At the beginning of the scene with Ghostbusters dressed as construction workers lowering Ray in the dig, Egon's left arm (the one operating the device) changes position between shots. (00:23:35)
Continuity mistake: Janusz is knocked off the ladder by Vigo's power surge. He then writhes on the floor as Vigo addresses him, alternatively touching the floor with his hand or not between shots. (00:22:30)
Continuity mistake: Peter got carried away playing with the kid, and his pitchy garbling summons Dana from the baby bedroom. He notices her and says something about a clear liquid; the tie of the baby bib is fully behind his back, but at the next cut the tie is across the shoulder. (00:19:10)
Character mistake: Ray and Egon are giving Oscar the check-up; Ray suggests to run a "Gammill and Pross Infant Acuity Test", which does not exist and is an inside-joke in the screenplay, since Tom Gammill and Max Pross are a duo of comedy writers. Egon agrees and says that they'll finish with an Apgar score, which is a real pediatric term - but it's a test for literal newborns, not an eight months old one like Oscar. (00:16:05)
Continuity mistake: In the first scene at the museum, Dr. Janosz Poha approaches Dana that is restoring a Bonington. In this first wide shot Dana is brushing a spot with barely any brown paint on it, but in the close-up that follows she's retouching a different part where the color is thick, and the left side of the painting looks different again when he touches her hair. (00:12:20)
Continuity mistake: During Peter's chat show, the second guest narrates a bizarre and kinda creepy story about the alien who dragged her to his room. She concludes the story with a disturbed expression on her face, but when the camera angle changes and Peter stands, she's actually smiling without any relation to the mood of the previous shot. It is in fact a direct continuation of the very first shot of the show. (00:10:20)
Continuity mistake: Egon is running his test on the married couple. He is about to write a note once his assistant has further tortured them with the announcement of another half an hour of wait. Sigourney Weaver has her arms crossed in one shot, but addresses Egon in the next shot having her hand on her chin. (00:06:15)
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)
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: The position of the socks (or whatever they are) sticking out of the suitcase when Peter presents the suitcase to Dana changes between shots. The one on top stick more in the second shot. (00:54:00)
Continuity mistake: When Peter talks to Dana and shows her the suitcase with her stuff (they sure seem to come and go as it pleases them from her home), Sigourney Weaver is holding the towel in a different way depending on the camera angle. (00:53:40)
Continuity mistake: When the Ghostbusters with their proton packs walk away from the car and get to the museum the morning after the bathtub incident, the people in front of the museum and on the stairs change at the cut. (00:50:25)
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)
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