Factual error: When the Archbishop arrives, Lenny greets him with "Your Eminence," which is a greeting for Cardinals. However, the Archbishop is wearing purple, while a Cardinal would wear red, indicating he was not a Cardinal. New York usually has a Cardinal for an Archbishop, anyway, and the production team likely just assumed the greeting without knowing the color rules. The correct greeting for an Archbishop would be "Your Excellency." In this case, either the greeting or the wardrobe was wrong.
Character mistake: Peter tells Egon over the phone that he gave Dana "300 cc of Thorazine." Besides the funny implications the movie ignores on how and why he was in possession of it, Venkman says "cc", but the drug is dosed in mg, so at the very least Venkman misspoke (that'd be 1/3 liters!). The line is not in the shooting script and other sources like the novelization just say that Dana had some valium lying around. (01:02:30)
Continuity mistake: When the possessed Dana asks Peter for the second time "Are you the Keymaster?", Peter comes in; notice that Sigourney Weavers' left hand is still at the top of the doorframe, in the reverse shot it's suddenly down. (00:56:10)
Audio problem: Running away from the 'bear', Tully shouts the humorous line; "I'm gonna to bring this up at the next tenants' meeting...there's not supposed to be any pets in the building." However, look at Rick Moranis' face; his lips are not moving and the line was dubbed over. (00:54:10)
Continuity mistake: Dana gets home and puts down on the table the paper bag with food and her coat as she answers the phone. She takes her shoes and pants off and the camera cuts away to a different angle where the coat and the paper bag have changed position. (00:51:00)
Continuity mistake: Dana witnesses the horrific appearance of Zool inside the fridge, and as she tells the Ghostbusters, slammed the refrigerator door shut and left. However, when Peter talks to her in the living room after he checked the fridge himself, you can see that the items on the table (the one by the TV she watched the commercial from) have been radically rearranged, something she surely wouldn't do leaving in a hurry. (00:19:00 - 00:26:55)
Revealing mistake: When the Ghostbusters are startled by the maid, they instinctively shoot their proton packs at her. You can distinctly see that the energy beam is coming -at - them and is not shot -from - their weapon, and it happens even before Dan Akroyd properly turned around and had any chance to point the 'rifle' part at the target's general direction. (00:31:45)
Revealing mistake: When Dana opens her fridge and a demonic dog opens its jaws to growl "Zuul!", you can literally see the outline of the lightbulb in the hound's throat. (00:20:10)
Continuity mistake: The silly bureaucrats cut power to the containment grid, which is about to blow up. Everyone runs away from the building; there are two main camera angles on the exterior, but they are obviously not in continuity - in the closer angle, natural light shines on the street to the right, while in the wider/higher angle that side of the building is in the shade. (01:07:50)
Factual error: Walter Peck in his slimy handshake introduces himself; "I represent the Environmental Protection Agency, the third district." The EPA has no 'districts' (NY's in Region 2). (00:46:15)
Continuity mistake: After Louis asks if anybody wants to play Parcheesi at his party, there is a lady sporting a red vest behind him, standing in front of a wall with framed photos. Two shots later, she's standing in front of the kitchen next to a bespectacled man. The very next shot, she's teleported back to where she was initially, in front of the wall. (00:53:25)
Continuity mistake: When Dana opens the door of her refrigerator and sees the temple with a terror dog, the shelf has a bottle with a green cap and a jar with a white lid at the end of it, but when Dana slams the refrigerator after the dog says "Zuul!", both items have disappeared. (00:20:00)
Revealing mistake: While the Ghostbusters ride to the building, there's a view of New York from the park under a red sky. Watch the buildings on the far left: They have a thick white outline around where the real sky was cut-out to allow for the new one to be put in. (01:18:35)
Continuity mistake: When the road cracks and swallows the police car, the distance between the ambulance behind increases and decreases between shots.
Continuity mistake: When the Stay Puft monster appears and all the cars crash, a driver goes out of a grey car through the window. In a closer angle he is back inside and repeating the movement. (01:31:15)
Continuity mistake: After the pavement cracks and swallows a police car, the chunks of broken pavement next to the car differ between shots. From a back view there are smaller pieces, but from a front view they are a couple of big and long chunks. (01:21:00)
Continuity mistake: When the Ghostbusters run out of the library, an old woman in a blue coat is seen on the left side by the bottom of the steps. A second later she is all the way up and coming from the right side instead. (00:12:20)
Visible crew/equipment: In the library scene, when the ghostbusters are walking towards the old lady to ask her questions, if you look behind Ray's head to the right you can see a set light with a white tarp in front of it on the second floor of the library. (00:07:35)
Revealing mistake: You wouldn't want to sleep inside the Sedgewick hotel, and not because of its ongoing infestation at the 12th floor; a small food cart rolls into a wall and that alone makes it wobble. (00:33:20)
Other mistake: After the trio stormed off the library, they are walking around the campus. As Venkman giggles mocking the "Get her" lack-of-a-plan, to the right of the screen there's an elderly lady who keeps staring curiously right at the camera. (00:12:20)
Answer: Chevy Chase, John Candy, Danny DeVito, Peter Falk, Mellisa Gilbert, Carly Simon, Teri Gar, and George Wendt, along with the four major stars of Ghostbusters themselves.