Revealing mistake: In the ballroom scene, when Slimer is flying around the chandelier, he disappears for a few frames when he reaches the far side. [This animation is mentioned in the DVD commentary. The film makers were generally unhappy with the entire animation and the fact that the representation of the apparition did not resemble those previous and that the movement was very unconvincing.]
Revealing mistake: Near the end of the film when the Ghostbusters take cover in a small corner and come up with the "cross the streams" plan, look closely at Peter's proton pack, you can see that it is a foam "stunt" pack as there is a small sticking out part that keeps squashing against the wall behind him.
Revealing mistake: The first time the heroes use their proton weapons (in the hotel sequence), you can see (using slow-motion) that the rays don't actually come of the weapon, but from their target. The rays were "drawn" during post-production and, apparently, it's easier to start drawing from the target to the weapon. (According to MM rules the use of slow motion IS permitted for viewing something significant, such as a 'revealing' mistake.)
Revealing mistake: A shot from above Dana Barret's apartment, from just above a statue looking down on the road below: The statue in the foreground is partially transparent. We can see the double yellow line on the street go straight through one of the statue's upper fangs, and one of the white lane dividers going through the statue's lower jaw. Viewed on Bluray disc.
Revealing mistake: As Dana's apartment crumbles apart to present the temple of Gozer, there is a tight shot of a gargoyle falling off an exterior corner. Carefully lined up with features on the gargoyle's face - but still readily visible - are the black strings that pull the gargoyle face off its mount.
Revealing mistake: When Louis throws the clothes on the gargoyle's head, the gargoyle is not standing on its 4 legs at ground level as it does for the rest of the film, but standing straight very tall, with the lower half of its body hidden inside a box, all intended to hide the obvious puppet mechanism.