Continuity mistake: Ethel Rogers drops the tray in the kitchen; the oven is open and many fumes come out of it. She kneels with her husband to salvage the food, and the vapors are gone. (00:09:20)
Continuity mistake: General Mandrake introduces himself and leans back against the chair, leaning back again in the next shot. (00:07:00)
Continuity mistake: The ferryman hands the letter to the butler; a left hand pops in frame to fetch it, but in the next shot the butler's outstretched arm is the right one. (00:04:00)
Continuity mistake: Mischa Auer is seasick, and feels even worse with the ferryman's snack right in his face. The man is holding the sandwich in one hand, and the other hand in frame is relaxed in his lap; however he has it on the rudder bar in the next shot (as he should with the sea in that state). (00:02:45)
Continuity mistake: During the boat trip at the beginning, wind knocks the hat off the judge's head in a close-up. The action happens again in the next shot, but it is starting with the hat reclined on the actor's face, flying across with a lower trajectory. (00:02:10)
Plot hole: Spoiler; Under the pretense to help catching the murderer, the Judge goes through great lengths to enlist the help of the doctor to fake his own death. In this adaption it's made moot by the fact that the murder happens in the living room, his body needs to be carried upstairs and we even see that happen, with all the remaining survivors hauling the 'corpse' in their arms. One thing is faking with a little make-up (literally a paste-on red dot) to be shot in the head, with just the accomplice examining the supposed corpse, and the others at distance and with bad lighting. But with everyone carrying the body, including a police inspector and a PI who are accustomed to violence and real murder, it's plain impossible.
Plot hole: Blore's death is fairly absurd, since the killer couldn't plan that he'd be standing, with all the possible room outside of the house, exactly in that spot at that distance from the window, with a ton of bricks that are precariously balanced on stone spheres that survived storms and heavy winds but somehow are loose enough to require a gentle push to fall down. (01:25:30)
Character mistake: The killer in the original novel (and as reminded also in this adaptation) stages his homicides following the nursery rhyme; goes through great lengths to do that, including planting a bumblebee in the room, using a hatchet, etc. But Blore's death has nothing to do with a bear, since he gets crushed by bricks. Conveniently the rhyme is not mentiones by the characters at all for his death, while they were the first ones to recite the matching verse in all the other deaths. In the original novel, Blore gets killed by a heavy object shaped like a bear.
