Revealing mistake: During the courtroom scene, one of the ghosts grabs the prosecutor and she is hanging upside down. Her dress comes down a little, but when she is about to fly through the door you can see part of the dress is pinned to her panty hose to stop the dress from falling off.
Continuity mistake: Near the end, the Ghostbusters make the Statue of Liberty smash the window on the roof of the art museum before abseiling in. The window gets completely destroyed, but just after Vigo says 'Now we become one' we see the window again and it appears less damaged than before.
Revealing mistake: When they gather around to watch what happens when you put the slime in the toaster, you can see when the toaster starts popping that it has little pneumatic pistons attached to the bottom, making it jump. When the toaster gets picked up off the table you can view its power cord which is entirely too big - more likely air lines.
Continuity mistake: In the scene where the Ghostbusters arrive at the museum, and Egon tells Peter what he's found about Vigo, while speaking to each other Peter gets a bag and hangs it around his neck. In the shot where you only see Peter's back you can easily see the strap hanging straight down. But in the shot where Peter's face is visible, he's holding up the strap with his hand quite high. Cutting back to Peter's back the strap is hanging straight down again.
Continuity mistake: When Dana and Oscar are at Venkman's place right after the scene where the bathtub attacks them, there is a slight mistake. Dana is shown from her left side, and she is holding Oscar. Oscar turns his head towards the camera, and almost immediately the view changes, and Dana is shown from her right side. Only thing wrong is that Oscar is still looking at the camera without ever turning his head.