Continuity mistake: When Mr. Russell interrupts Hastings' plans of randomly shooting in the middle of the Alexandria harbor, an empty brandy glass is on the table next to him in the first shot, and comes closer the second time he's in frame. (the two shots are not strictly consecutive but there's no reason why the frail old man, still in the same position both times, would pull his empty glass a couple inches closer when off-camera). (00:26:20)
Continuity mistake: Clapperton demonstrates how he can deal cards of his choosing at will and therefore he refrains from playing bridge. In the close-up of his hand and table you can see the cards he dealt are stacked irregularly, but when he deals the last 4s the cards are more neatly arranged, spread in a fan. (00:17:10)
Plot hole: In the original novel, the victim's voice is described as "shrill." In here, it's quite the opposite. When the trick for the alibi is performed, the relevant lines are not read by John Normington, thus Poirot's exposition at the end, with the girl providing the voiceover, indirectly further exposes its unbelievability.