Continuity mistake: When they are chasing the 'muncher' ghost down the street, the light bar is only seen flashing on the Ecto 1 when seen from inside the restaurant. The rest of the time they are not on. (00:59:00 - 00:59:30)
Continuity mistake: The mini Puft makes a hole in the marshmallow bag between the letters H and M. In further shots the hole is fixed and it's now between the A and the L.
Continuity mistake: While driving around the city, Trevor wonders if the ghost wasn't really a racoon. Podcast has his ecto-googles on his head, but a shot later, when Trevor suddenly stops, he has them on his eyes.
Continuity mistake: When we first meet Phoebe she is fixing a plug, body tilted to the right, left arm raised. A shot later her body is tilted to the left, left arm in a different position.
Continuity mistake: When Gary is testing the trap on the car, he puts his hand very close to it. A shot later it's further away, and he's reaching for the trap again.
Continuity mistake: When Dana asks Venkman if he marked the cards her right hand is away from the electro-shock generator in the front shot, but suddenly on top of it in the angle shot from behind.
Continuity mistake: When Gary and Callie are having lunch, there's a waitress behind him that passes next to him. When she's next to Callie, shot changes, and she's now a meter behind, approaching Callie again.
Continuity mistake: After Gus drops the trap his body is closer or further away from it and his right hand is close or away from the trap. This changes back and forth all the time.
Continuity mistake: When Grooberson drops the trap in front of the kids, the handle points at Podcast. A shot later it's in a different position, parallel to the kid. Also, the cable's position changes several times.
Continuity mistake: When Gary and Phoebe are trying to open the trap the two cables hanging down the fender and bonnet are either close together or apart, depending on the shot.
Continuity mistake: When Gary shows the kids a YouTube video of the Ghostbusters, he points his finger at the screen. From the opposite angle his finger is away. Then back to the wide-angle, and he's retrieving his finger again.
Continuity mistake: Callie finds the 'secret' (even if it's in plain sight, really) basement with Egon's stuff following the instrument she found in Phoebe's room. She has the tool with her, she does not have it with her when she is possessed, but it is back at the house when everyone else is home.
Suggested correction: Most likely, Egon's ghost returned the PKE Meter to the house, knowing how important it would be to help fight Zuul.
Continuity mistake: At Walmart, when Gary finds the sentinel his eyes are looking down. There's a close-up of him slowly looking upwards and finally staring at the creature. Shot changes, and he is looking down again and repeating all previous movements.
Continuity mistake: Trevor is driving the Ecto-1 and complains that Podcast is breathing on him. We see Podcast very close to him. The shot cuts and Podcast is now further away.
Continuity mistake: Phoebe and her mother are by the door of the farmhouse, waiting for the pursuing demons to appear. The shoulder strap of Callie's dress is lowered in most shots, but goes back up suddenly (and only) in an intermediate shot.
Continuity mistake: When Gary is freed from his ghostly form he says "Oh, that was weird" and a shot later his left hand is suddenly next to his face.
Continuity mistake: After testing the proton pack, Phoebe raises her hand to adjust her glasses. A shot later her hand is lowered.