Gasoline in a sealed container lasts 3-6 months before it starts to break down, high octane (ethanol free) gas starts to degrade after 9 months. Diesel has a 12-month shelf life before it starts becoming sludge. Once these amounts of time have passed the fuel will burn inefficiently and cause damage to the engine, severely limiting how long it will run before serious engine damage occurs. When it comes to gasoline, after a year at the most it won't be combustible at all, so after 20 years there is no way they could siphon usable fuel from those cars.
When Joel shows Ellie how to use the pistol she found, he fails to teach her a few critical things. He shows her how to properly grip the pistol, but neglects to show her how to hold her arms, amateur shooters tend to hold a handgun close to their body, when it's much more accurate for their arms to be extended. He also fails to show her the proper shooting stance, the way a person stands and how they position their upper body can affect their accuracy almost as much as how they hold and grip the gun. He also doesn't show her how to use the safety, how to properly and safely uncock the hammer when a round is chambered, and how to lock the slide open if the gun has a jam that needs cleared. After he gives the gun back to her, Ellie puts it in her back with the hammer still cocked, which is a dangerous way to carry that kind of gun if the safety is off. Joel comments on how FEDRA's firearms training is inadequate, but he needs to take his own advice in that regard.
Kansas City is frequently portrayed as being near mountains, as it is in this episode. However, Kansas City is on the prairie: to get to mountains as they're shown, you would have to drive several hundred miles.
After the roller coaster (which is in Kansas City), the following shot shows an elevated railroad trestle. There is no structure like that within two hundred miles of Kansas City in any direction.
Joel is paranoid enough to spread broken glass to act as an alarm, and yet he and Ellie bunk down in full view of the door, where anyone passing by could see them, and shoot them.
Joel says that FEDRA used a vehicle with a plow on the front to push abandoned cars off the road. However, all the cars are neatly parked, rather than haphazardly scattered as if pushed aside.