Audio problem: Abby is yelling at the ghosts that she doesn't like one, and then "I don't like you either" to another one. The ADR is so off that almost no words match up with her mouth movement.
Continuity mistake: At the mansion, the tour guide hits the square on the wall twice.
Continuity mistake: After the meeting with the ghost of the mansion Erin hugs Abby and she gets the ectoplasm from her, but in the next shot it disappears.
Continuity mistake: As they walk through the frozen soldiers the black guy on the right side opens and then closes his eyes. (01:32:50)
Continuity mistake: When Patty is sitting in the booth and Kevin says she's there, in the next shot Kevin is messing with a rubber band and Erin asks him to answer the phone, in the next shot he is not holding the rubber band. (00:40:13 - 00:40:36)
Continuity mistake: Garret the tour guide gets burned on his hand. After he breaks the square his hand isn't burned.
Continuity mistake: Erin steps on ectoplasm in Eldrich's house, but the goo disappears in the wide shots.
Continuity mistake: The position of the flashlight that Patty drops after seeing the ghost in the subway tunnel for the first time changes between shots.
Continuity mistake: When they arrive at the concert and are taken downstairs, the guy is explaining about Fernando. If you look at the high voltage strap she is wearing the writing changes to right way up to upside down then back again between shots.
Character mistake: When Erin pops Stay Puft, the girls get up. One of the girls says "welcome back" to Erin. She didn't leave the group.
Continuity mistake: At the beginning while Erin talks with Fillmore her right hand moves between shots.
Continuity mistake: An early shot of the Chinese Restaurant shows an open garage and the white bonnet of the new Ecto-1, despite the fact the Ecto-1 had yet to be introduced into the movie at that point.
Other mistake: After the ghost "possesses" the building and blows out the windows, no shards of glass or debris land on the Ghostbusters as they get up to escape, even though there was plenty of time for the glass and debris to rain down on them.
Suggested correction: You can plainly see that the debris is actually flowing upwards in defiance of gravity. Spectral energy is running amok and the laws of physics are all over the place.