Plot hole: When the Allies blow up the airfield they pour gunfire from the backs of the trucks into the tents where the Japanese soldiers are eating. If you watch carefully you will see that the Allied guys in the truck nearest the screen are pouring lead through their comrades in the other truck. Another classic case of 'friendly fire'.
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 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: Eros makes it very clear that his race does not 'cling to life.' If this is the case, then why is he so determined to save everybody?
Plot hole: The radar operator reports a bogey at 15,000 yards, without, at first, giving a bearing, yet everyone on the bridge immediately looks to the starboard bow.