The scene with Christopher Plummer shooting a rabbit in the woods was filmed in New Jersey and not Devon, where the rest of the film was shot. This was a scene added after principal photography had been completed--and Plummer could not return to work in England for tax reasons.
Agatha Christie's daughter, who had approval of the script, was initially concerned that Michael Elphick's police inspector, modeled to some extent after a harder-nosed American-style police officer, would prove unpopular among the local constabulary in Devon, where she lived.
The source Agatha Christie novel was one of her favorites of the ones she had written along with "Crooked House" (1949).
Dave Brubeck replaced Pino Donaggio as composer. The original score was not by Brubeck but by Donaggio, who wrote his typical lush and beautiful music. When the film didn't test well, the producers decided to jettison the Donaggio score and replace it with Brubeck's music. Brubeck was told he'd have two weeks to write an original score. He said no. They then agreed that they'd use already existing Brubeck tunes and newly record them. His jazzy muzak score was often negatively received by both critics and audiences.