Lauren Bacall killed Piper Laurie and then she kills herself.
Continuity mistake: When Nanny Taylor is discovered in the bath and Poirot is leaning over her, her plait is first across her chest and then it is suddenly along her arm. This is most evident in the flash-back scene at the end of the movie.
Hercule Poirot: People like to talk, and in doing so they tell the truth. It puts less of a strain on the memory.