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)
Other mistake: After the guys decide to rent the building, the shot of New York from the park is the very same one, though with different sky colour, to that of the moment when they are about to battle Gozer. Though it's a very wide and common shot of the park, the very same people are laying on the grass in the very same position in both shots (big screen recommended to spot it). (00:16:45 - 01:18:35)
Other mistake: Winston Zeddemore's surname is spelled as "Zeddmore" in the closing credits. (01:43:50)
Answer: He places it on the altar just after they believe they have vaporized Gozer with the proton packs. At this point, thinking the ghost to have been destroyed, he sets it down as he believes the job is done and he will not need it.
Jazetopher