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.
Plot hole: After Ann retrieves Tibor Zoldan's music box from the pawn shop, she finds the incriminating photos of her Nazi father, Michael Laszlo, hidden in it. Even though Zoldan (who had died) could have redeemed the music box from the pawn shop within a certain time period, it makes no sense that he would have pawned it with the photos left inside. The photos were how Zoldan was able to blackmail Laszlo. It's highly unlikely he would have forgotten they were in there.
Plot hole: The odd couple tails the suspicious guy bossing around the car company mogul and run a check on the license plate. The response is "Car registered H.W. Scully. No known residence, only address PO Box 25047 Detroit." They tail him a bit, end up in the bowling alley and lose him in the commotion. After that, Leno asks his buddy at the district if he has "anything on that guy Scully", and the answer is "This guy has done anything but rape Bambi. Several weapons charges, assault and battery, he beat a murder rap in Sarasota" etc. And of course, an address. (00:56:35 - 01:01:35)
Plot hole: When the teens in this film come to camp, they see in the bathroom a sign spray-painted by one of the kids from Part 2 that says "Fuck Angela Baker." This doesn't make sense because in the second film everyone only knew her as Angela Johnson. So the sign should have said "Fuck Angela Johnson."
Plot hole: Given the store's being bought by a retail chain like Kroger's there's no reason Bill's partner can't sell him his share in it, get half the price they're receiving for it then have Bill make quarterly payments to him. They could've also got the new owners to keep Bill on as manager as well as keep their employees or void the sale.