Plot hole: When Eve is being led out to the airplane, she bolts when two shots are fired from inside the house (presumably Anna firing at Thornhill, not realizing that the gun was loaded with blanks). Moments later, she jumps into a car driven by Thornhill, and they escape together. There is no way Thornhill could have gotten there that fast, given that he was in the house only seconds earlier.
Plot hole: They all drop their backpacks and bags 3/4 mile down into the hole before climbing by rope into the caverns to begin their journey. Later in the movie, they are all sitting deep in the caverns complaining about the lack of water supply. Suddenly the long-haired guy pulls out a large glass bottle of gin, completely intact and they all drink from it. There is no way his pack could have fallen 3/4 mile onto a hard surface without that bottle breaking.
Plot hole: When the flying saucer first appears, it is supposed to be 4 AM. But the grave diggers are still there from the burial of Bela Lugosi's wife.