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.
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.