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: 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.
Plot hole: Even if Dr. David Trent's and Annabelle Loren's elaborate plan had worked flawlessly (framing Nora Manning for Frederick Loren's death), the fact remains that they faked Annabelle's death for everyone to see, which would immediately arouse suspicions for investigators. Even if Annabelle and Dr. Trent somehow fled the scene before the police arrived the next morning, their actions would still raise many questions that implicated them; thus, their clumsy and convoluted scheme was far from being the "perfect crime" they imagined.