Dr. Armstrong exits his car and walks past Marston's Jensen twice, in the harbor scene.
When the list of suspects is being typed for Blore, the order reads, "Judge L.J. Wargrave. Anthony Marston. Philip Lombard." ... so forth. When Blore makes notes next to the names later, "Thomas and Ethel Rogers." comes before "Anthony Marston."
Fred Narracott walks up the dock steps twice.
Thr doctor hands Mrs. Rogers a cloudy glass. When she drinks it it's clear.
The letter in the opening five minutes is typed 'U.N. Owen.', but when the signature is shown, it is written as 'U. N. Owen'.
When we see the envelopes of the letters to the Ten Little Indians being franked, it appears that the sender (rather than the postal sorting office) is doing the franking. Also, the franking mark is made entirely on the envelope itself, when the reason for franking is to overlay the stamp with a franking mark to prevent it being reused.
When Marston begins to choke, one of the guests grabs Marston from behind as if to administer the Heimlich Maneuver. The Heimlich Maneuver wasn't a known way to help choking victims until 1974.
When Dr. Armstrong is checking Marston's body for signs of poison, Blore says that the Kiss of Life would be useless at this point. Mouth-to-mouth resuscitation was only introduced in 1950 as a life-saving method; prior to that, other methods of artificial respiration were used. The term "kiss of life" itself only came into popular usage sometime in the 1960s, while the story is set in 1939.
The term "gung ho" was not widely used in 1939. It didn't begin to be popularized until several years into WWII.