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.
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.
Continuity mistake: When Dr. Venkman is looking in Dana's refrigerator the items on the top shelf shift position, disappear and/or are replaced with other items. The large glass dish that was on the left of the Coke can is replaced by a small plate of food. The Coke can turns. There is also now a large bottle behind the Coke can. Clearly these 2 connected shots were filmed on different days and the items were stocked without regard for the previous shots items and positions.