In the close-up of Ecto 1A's license plate near the end of the film, the Statue of Liberty is in the middle of the plate. In all other shots, it's on the left side of the plate.
Peter and Dana are waiting for a taxi outside Peter's apartment building when the Ectomobile pulls up. The license plate on the front says ECTO-2. The revamped Ectomobile was intended to be called ECTO-2 but was later changed to ECTO-1A. The scene must have been shot before the change was made.
When Ray, Egon, and Winston enter the room with the heads on poles, Winston's helmet disappears and reappears between shots.
The carriage with Oscar stops on First Avenue, and shops are in the background. Ten minutes later, when the Ghostbusters are digging in the street, a parking lot is in the background.
At the end of the film, when the Ghostbusters get into the museum, the Statue of Liberty is standing. Once inside, the statue is laid down next the museum, but nothing was seen or heard. Based on her raised arm, the statue alternates between laying facing up and face down between shots.
(at around 1h 14 mins) When Janine, Louis, and Dana are in Peter's apartment watching a movie, a window opens in the room with the baby in it. Dana feels the breeze on the back of her hair and goes to investigate/check on the baby. Considering the door to the baby's room was closed and none of the other windows in the apartment appear to be open, there is no way she could have felt that breeze.
The camera Peter (Bill Murray) uses to take pictures of the painting (a Brooks Veriwide) would not be appropriate for this kind of photo shoot even though the description of the camera says (when used properly) : "It's great: it's very sharp at every aperture, there is no distortion and there are no ghosts.'' .
(at around 15 mins) During Oscar's examination, Egon suggests they perform an "Apgar score" test on baby Oscar. However, Apgar score is a test made on newborns only (usually 1 and 5 minutes after birth), so such a test would be entirely irrelevant in Oscar's case. This is a gag to show that the guys don't know what they're talking about.
Early in the film, Frank tells Dana "I'm not the doorman, Miss Barrett. I'm the building superintendent." At the end, Michael P. Moran is credited as playing "Frank the Doorman." It's a joke, to acknowledge what he said at the beginning.
In the statue, Peter stands next to Winston, who stands next to Ray, who stands next to Egon. It the next shot, Winston is next to Peter, who is next to Ray, who is next to Egon. In the following shot, they're back to their first configuration. Considering the space and the amount of time passed, it's entirely possible that they deliberately changed places.
(at around 1h 26 mins) When asked if she (Lady Liberty) can go faster, Ray denies it because the vibrations could damage her. Presumably, she got off the pedestal on Liberty Island very slowly and carefully, using all four limbs.
When the Ghostbusters drop in to the museum, Ray and Winston both have lights on their "slime throwers". These lights switch from on and off between shots until the end. The proton packs have activator switches on the wands, to conserve power, so the slime throwers could have the same.
When Ray and Egon run the photo of Vigo through the spectronalyzer, the analyzed version of the photo is completed when the original photo is halfway in the machine.
When Egon, Winston, and Ray enter the cavern of slime, they kick down a wall of rocks. While looking around, Ray sits down on one and it squishes.
The movie takes place in New York in December, yet the city has very little snow and few Christmas decorations.
When Venkman steps on the pedal to trap the "jogger ghost" activate the ghost trap, his foot misses the button, but the trap opens anyway.
The trap is actually opened by the pedal switch next to that "button".
The power cord to the computer on Janine Melnitz's desk is not plugged into the computer.
There is no reason why Peter would be arrested for disturbing the peace alongside the rest of the crew, when he was simply having dinner and they showed up and caused the issue, yet Peter is arrested alongside them.
There is no reason for massive crowds and barricades to be at the Museum during the final showdown-especially when New York City is shown to be beset with ghosts terrorizing everyone, and supernatural occurrences taking place everywhere-yet thousands of people are there, inexplicably.
There is absolutely no reason why Ray would have a cigar in his hand as he speaks to the Mayor-having just gotten arrested and then transported to see him-yet he holds one during his allotted two minutes to speak at Gracie Mansion.
If the Statue of Liberty were to walk around like a person, as depicted in this film, the statue would break and crumble at the joints.
When the slime begins to activate in the court room, it inexplicably causes heavy, sustained gusts of wind to hit the Ghostbuster crew, altering their hair and moving their clothing, yet no one seems to notice.
The "City of Albany" ghost train, which is said to have derailed and wrecked in 1920, consists of a late 19-century locomotive and cars. Railroads still used that equipment in 1920, but a "name train" would have used modern, up-to-date equipment.
Janosz tells Venkman that the painting of Vigo is being prepared for the "Romantic exhibition," which would date it no earlier than the late 18th Century. Given that it's a self-portrait of a 16th Century tyrant, it would properly be classed as Renaissance art.
In the courtroom, when one of the ghosts flies through the wall behind Ray, Egon yells "behind you, Ray!", but his mouth says something else.
When Dana gets to Peter's house after the bathtub scene, Oscar is crying. In closeups, the baby is not crying.
When Raymond and Egon arrive at Peter's rendezvous with Dana, they tell Peter about their plans to go underground. Ray clearly speaks to Peter, but only Egon's mouth moves.
When Dana is talking to Frank at the beginning, she says "You're also a human being, Frank." Whilst she can be seen mouthing the word 'Frank', she cannot be heard saying 'Frank'.
Near the end, when Vigo moves the boxes and other items to reveal where Oscar is hiding, part of someone's arm pops out from behind the pillar at the left side of the screen.
When the jar of pink slime starts to boil In the courtroom scene, the mechanism and pump making it move are visible.
The camera crew is reflected in the dancing toaster.
Small pegs jut out the bottom of the dancing toaster.
(at around 1h 16 mins) During the "Flip City" song montage, when the large monster ghost is coming through the arch, the green screen to the right, at the top of the arch, is still visible.
When the mayor is looking out the window from his office, the eclipse appears to be over Central Park as seen from Central Park West. City Hall is downtown, too far to see Central Park.
When the Ghostbusters are being brought to City Hall, the police car has red and blue emergency lights. New York City police cars have red and white emergency lights.
When the Con Edison Supervisor and the police arrive at the hole on First Avenue, a subway station exit nearly has red lights on top. The only one subway station on First avenue is the L train, and all of the exits to that station have green lights on top.
People still don't believe the Ghostbusters found slime underground at the trial many days later. In order for the real electricians to get the city lights working again, they would've had to go underground to do all the repairs in the location where Ray caused the damage, and they would've discovered the river of slime for themselves.
It is established that no one believes in the Ghostbusters or the paranormal. However, in the first movie the citizens of New York were terrorized by ghosts, the Staypufft Marshmallow Man, and supernatural forces in the sky above the skyscraper when Gozer came to Earth. Reporters even filmed the events. Five years later, no one believes anymore.
When the Ghostbusters arrive at the museum in The Statue Of Liberty, they descend from the crown on ropes. The windows on the crown are not large enough for them to fit through on their own, much less with their equipment.
Hardemeyer has the Ghostbusters committed to Parkview Psychiatric Hospital for observation, claiming to be acting on the mayor's behalf. A mayor's office does not have the authority to commit an individual. Also, three of the four Ghostbusters are doctors of psychology, making it highly unlikely that the hospital would admit them without question or suspicion.
There is no way the Statue of Liberty could have been hotwired to be made to walk, and certainly not within the short time span the Ghostbusters had to do so before midnight, simply by spraying it with slime and playing music.
Ray, Egon, and Winston go down into the sewer to examine the slime. Winston is using a measuring device to see how deep it is when he is pulled towards the slime. Egon and Ray try to hold him back, and one of them calls Winston "Ernie."
When Louis is being outfitted with a Ghostbusters jumpsuit, the name tag says "Spengler" and it is the correct size, even though Egon is about a foot taller than Louis.
In the case against the Ghostbusters breaking their restraining order, the court never bothered to have Dana testify. She asked them to help her and Oscar, making her an accessory to them digging the 1st Avenue hole.
When Peter is trying to hail a cab, he's standing on a one-way street, yet he's facing the opposite way of the direction of traffic.
The dock supervisor reports that the Titanic is arriving at Pier 34. It was scheduled to arrive at Pier 59, one of the few docks at the time large enough to accommodate her.