The Union and Confederate soldiers in the episode were carrying historically incorrect flags. The thirteen star "Betsy Ross" was flown during the Revolutionary War, not the Civil War. The "Stars and Bars" was used by the Virginia Army but never in Louisiana.
When Ecto-1 is seen from behind riding in the rain towards Muddy Flat, the license plate reads 'Acto-1'.
When Ray is using the Makeshift Proton Pack, the proton stream was missing when alarm is going off or the proton noise was wrongly still there.
When the Ghostbusters are talking with Marie Gautier at the diner, the shot changes from Winston to Peter, but the background remains the same.
When Egon's watch is seen from his point of view, Winston and Peter become out of focus in the background. But when Egon puts down his arm and the focus switches back to Peter and Winston, Egon's arm becomes see-through.
While Winston is holding the makeshift trap Egon touches it and gets shocked, but while Winston is holding the trap he is not shocked.
When Egon is using his extra PKE Meter, it has an electrical cord attached which has never been there before. Egon is also using it outside and wouldn't be able to plug it into anything.
During the prehistoric flashback, Egon refers to the marine predator as a Megalodon, which was a prehistoric shark, though what attacked them was clearly a reptile.