Albert Aachen climbs to the top of the diving boards during his aquaclown rehearsal, picking up a bottle with his right hand to take a swig from it, with the left theatrically outstretched. The shot changes to a close-up, and Aachen now has the bottle in his left hand. He smiles and the shot changes to a long one - where the bottle is now back a few steps behind him on the platform as he dives.
The level of sherry in Poirot's glass changes from half empty to almost full while he's in Sir Carmichael Clarke's living room.
The sleeping Mrs Fortune's mouth changes position from shot-to-shot, and occasionally doesn't match the snoring soundtrack.
Japp's opening of Betty Barnard's bathroom door makes the wall and mirror shake, revealing it as a studio set.
For the swimming pool murder, when the dart is fired, the view is from behind the murderer and one can plainly see the gun is aimed below and to the right of the victim. Then in the close-up of the victim, the dart is positioned on the left side of his neck as if it had been fired from his left, not mainly from his front. In any case, it is a very unlikely shot with a dart pistol from such a long range.
As Tony Randall is climbing out of the trunk of the car that he was hiding in, the tail lights are clearly on. But when Robert Morley is sitting in the car the tail lights are off. In 1965, automatic headlights were not yet available for cars, especially cheap models like this one.