Poirot claims that Daphne could not possibly have seen in the mirror Kenneth Marshall sitting at the desk typing. However, the next shot is of the desk from Daphne's viewpoint and the typewriter is clearly visible. If Kenneth had been typing, his hands on the keys would be in view, and if he were leaning forward, a large part of his body would be as well.
The first time Patrick and Christine Redfern are heard arguing about Patrick's relationship with Arlena, Patrick says "I can't even speak to a pretty woman without you jumping to the conclusion that I'm having an affair with her". Later when Poirot flashes back to the scene, Patrick is heard saying "I can't even speak to a pretty woman with out you jumping to the conclusion that I'm... well, having an affair with her." The scenes are supposed to be identical but they are not.
When Patrick wants Myra to take the speed boat back, she says that she doesn't know how to drive it. He gives her a very quick lesson. When he discovers that Arlena is dead and asks her if she can go get help, she is suddenly quite proficient.
In the film, Patrick Redfern was wearing swim briefs ("Speedos") on many occasions (suntanning on the beach, steering a motorboat with Myra Gardener on board), and it is suggested that, since the film was set in the 1930s or 1940s, that the male "overall" swimsuit was "norm", and the "Speedo" type suit was an anachronism. This is not true; by 1936 (after the Olympics) men started wearing one piece and much tighter fitting "Speedo" suits. The film is probably set before 1939 (the book was written in 1941), and by this time, fashionable and daring men would have worn this type of swimsuit, particularly to secluded getaways, such as the setting for the movie.
Patrick Redfern could not have planned in advance that anybody (in this case Myra Gardener) would ask for a ride with him in the boat and then be his essential witness. I have not read the novel and don't know if the same mistake is found in the book, but it is a big hole in the film scenario.