The Judicial Hanging as witnessed by the Judge is totally wrong. What is shown is a "short drop" hanging with an American style rope with the coiled "Hangman's Knot" above the noose. British Judicial Hangings used a slip noose with no knot, and more importantly, the "measured drop" system, whereby the length of the drop was calculated according to the weight of the person. In practice this was between six and ten feet, therefore the hanged person would drop through the trapdoor into a chamber below. The hood was white, not black, and to "refuse" it was never an option - its use was part of the Home Office execution protocol, placed over the head prior to the noose so it did not fly off during the drop. And a judge being permitted to pop in and look the condemned person in the eye would simply never have happened.
When the condemned man is hanged in Judge Wargrave's flashback, he is shown dropping about two feet before the rope goes tight. In reality, the rules of public hangings established in the middle of the nineteenth century in Britain specified a drop of approximately six feet (adjusted for the height and weight of the victim) to ensure a clean snap of the neck at the end. A drop of two feet would have resulted in the executed man strangling slowly over about twenty minutes.
Near the end, when Vera drops the gun (to the accompaniment of a loud crash) the barrel of the gun wiggles, proving that it is rubber.
Because Vera and Lombard do not move Armstrong's body out of reach of the tide (as they do in the novel), when the police do arrive on the island, they will have no reason to assume that Armstrong was not Mister Owen, as there will be no evidence that someone was on the island after he was dead.
In the final scene, Mr. Owen has replaced all ten figures on the dining room table, having retrieved the "missing" ones from wherever he had hidden them. Why didn't anyone find the five missing ones during the search at the end of the previous episode?