Audio problem: During the Walmart scene, it seems they edited in Gary saying "Oh, God." However, it's over no visible mouth or throat movements. (01:15:17)
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)
Visible crew/equipment: When Trevor is uncovering the ECTO-1, you can see the camera's shadow on the left of screen and even briefly on the car front.
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.
Other mistake: In Walmart, some mini-Stay Puft Marshmallow Men turn on a propane grill and set each other on fire. Gas grills on display never, under any circumstances, have propane tanks installed. This would create an obvious safety issue because there is nothing keeping a customer from accidentally (or deliberately) starting the grill and causing a fire. Additionally, propane tanks are never stored inside for similar safety reasons.
Other mistake: When Trevor attempts to start Ecto-1's engine the camera shows a very incorrect engine. A Triumph Herald/Spitfire 4 cylinder that is less than 1 to 1.5 litre.
Character mistake: There are signs out front as the Spenglers arrive at the dirt farm. One of the signs is a call back to a scene in Ghostbusters 1984. In the scene, Ray quotes the book of Revelation: "And I looked, and he opened the sixth seal, and lo, there was a great earthquake. And the sun turned black as sack cloth, and the moon turned blood." When Finn Wolfhard reads it he misquotes the line saying "The sun became as black as cloth."
Deliberate mistake: The mother jumped through the window, shattering the glass, but did not get cut or tear her clothes. (01:28:55 - 01:31:10)
Other mistake: Egon's old jumpsuits fit the kids perfectly, but he was a grown man and these are young children.
Other mistake: When Phoebe calls Ray from the police station, Ray says the firehouse is now a Starbucks, but during the end credit scenes Winston is standing in the firehouse and Ecto 1 follows him.
Suggested correction: Ray was being sarcastic. A common joke in NY is that every time a business closes, the location becomes a Starbucks.
Suggested correction: This mistake has already been corrected. Starbucks is often used as a shorthand joke about general gentrification, companies going out of business, company over-exposure, etc. (Which is kinda based on reality. Ex. In my hometown there are literally four Starbucks locations over a 5-mile stretch of road, at least one of which I believe took over an old store that closed down. It's utterly insane.) Ray isn't being literal when he says the firehouse is a Starbucks - he's just making a sarcastic joke about how it's closed down.