The ship used for filming is the motor yacht "Madiz" built in Scotland in 1902 and is privately owned. In World War 2, the "Madiz" served in the British Royal Navy as a Royal Patrol yacht.
"Problem at Sea" was first published in the USA in This Week, 12 January 1936, then as "Poirot and the Crime in Cabin 66" in The Strand, February 1936, then republished in The Regatta Mystery and Other Stories.
The plot comes from one of the stories in the collection "Poirot's Early Cases" (1974).
Mr Tolliver (Geoffrey Beevers) and Mrs Tolliver (Caroline Johns) were husband and wife in real at the time of the recording of this episode. Both also had a major role in Dr Who. Geoffrey Beevers played the Master in THE KEEPER OF TRAKEN against the Tom Baker Doctor and Caroline Johns played Elizabeth "Liz" Shaw, companion of the Jon Pertwee doctor.
Sheila Allen (Mrs Clapperton) previously played Lady Diane Clarke in The Alphabet Murders (1965), a loose, comedic adaptation of "The ABC Murders" starring Tony Randall as Poirot.