Bums: Making a Mess All Over the City - S3-E14
Factual error: Charlie drops the moltov cocktail into the police car in the end, light enough so that it doesn't break, but the car explodes about ten seconds later, as Charlie explains he had soaked the entire inside with gasoline. However, there realistically wouldn't be such a long pause as shown in the show for the gasoline fumes to ignite. Also, the explosion is much more powerful than it realistically would have been, revealing pyrotechnics were used. Obviously done for comedic value, but still a mistake.
The Gang Solves Global Warming - S14-E10
Factual error: When Charlie and Dee go to get ice, they go to a "liquor" store, down the road. In Pennsylvania, all liquor stores are state run, called "Fine Wine and Spirits", and only sell liquor and wine. In this scene, ads for liquor, beer, and wine are all on the outside of the business. Liquor stores in PA do not sell beer.