Episode #1.1 - S1-E1
Continuity mistake: As the guests enter the house for the first time, Doctor Edward Armstrong in his white suit is amongst the first ones to go through the door. Philip Lombard is right behind him, and he walks past the door when the doctor reaches for his hat - but in the next shot, the doctor already has his hat in hand when Lombard hasn't gone past the door yet. (00:12:45)
Episode #1.1 - S1-E1
Continuity mistake: The unsuspecting group is on their way to the mansion. The ferryman goes back to his boat leaving the luggage he was carrying in the middle of the meadow. Judge Lawrence Wargrave asks "Davis" to take his suitcase. Davis picks up the judge's black suitcase in his right hand, switching his brown one to the left hand. Next shot and it's the other way around; he carries the judge's in his left and his own with his right. (00:12:20)
Plot hole: There are several parts of the murderer's plan that are based on pure convenience and/or against all odds, moreso than in the novel due to particular choices in the aesthetics or plot. The murderer (who can't exactly sprint around with cat-like motions) gets to the General and kills him in a gruesome manner, reaching a victim entirely in the open, with the island lacking any cover, not even a tree. Vera happens also to scream providing a diversion; unlike the book, the killer does not do anything to induce her hallucination and split the group, nor sabotages the lights creating a dimly lit environment that makes the trick more plausible.
Episode #1.1 - S1-E1
Factual error: Unlike Christie's novels, there is no explicit statement of the date - the original novel started on the August 8th, which is compatible with what is shown here; Vera is interviewed and the letters are all posted on August 2nd 1939, which would fit. However, there's a problem when Vera changes seats en route to Soldier's island. A passenger is reading the Daily Express, and the headline is from August 29th of that year. Too much time elapsed and it's the end of the Summer while the chat between Emily and Vera implies otherwise; it's also Tuesday but the doctor comments "It's been a long week" when he apologizes at dinner - the weekend feels a more appropriate time for a party and gathering as shown. (00:06:15)
Episode #1.3 - S1-E3
Plot hole: The killer is meant to create the perfect crime, but the angle of the shot would make obvious to any forensics examiner that it's a suicide. There is practically no possibility for a person supposedly positioned across a long dining table to kill someone else with a shot under the chin. (00:55:50)
Episode #1.3 - S1-E3
Deliberate mistake: When the judge shoots himself, the revolver slides across the table, to fake his murder by someone else. But there is no mechanism in place that explains how he does this, making it appear as if he is able to accurately throw/slide the gun after shooting himself. In the original novel, he used a rubber band to achieve the effect, but he is not shown setting it up here.