Revealing mistake: In the film's first scene, as Clark and Russ Griswold make a left hand turn to pull into the used car lot in Chicago, the upper quarter of the screen shows mountains and palm trees in the background, which is an impossibility for Chicago. I believe the nearest mountain range to Chicago is in Arkansas and the nearest palm trees reside in Louisiana. (This scene was filmed in California, which explains the mountains and palm trees, BUT nonetheless a mistake.)
Revealing mistake: In the scene where Clark ties the dog to the bumper of the family truckster, Rusty hands the leash to Clark while the dog is chewing on his leg. The camera changes to show Clark's face close up, and when he pulls the leash to free his leg from the dog, you can see the end of the leash fly behind him (with no dog attached.)
Revealing mistake: In the scene where the Griswolds tie Aunt Edna to the roof of the car in a sitting position and drive her body in the pouring rain, pay close attention to the back of her head (which is not covered like the rest of her body). It's easy to see that it's a mannequin, with the pure-white plastic skin. Also, the mannequin's hair is very short in the back, whereas Aunt Edna's is longer.
Revealing mistake: In the scene where Chevy Chase is walking through the desert searching for a gas station he falls down and ends up staring at a skull next to a small fuel tank. If you look closely, you can see two springs on both sides of the inside jaw. This is obviously a skull model and the springs are there to keep the lower jaw shut tight against the upper jaw.
Revealing mistake: At the gas station, while Clark watches the mother and son refuelling the car beside him, she points at her son to remove the gas cap. If you watch closely, he looks like he unscrews it but he has nothing in his hand, and when he "places" it on the rear bumper, in the next shot there is nothing sitting on the bumper.