Revealing mistake: The letter which is typed on the Olivetti portable typewriter (certainly an accurate model for this period) is obviously a modern laser-printed letter, not from a manual typewriter.
Factual error: The opening scene is shot on a rooftop on Central Park West in New York City. The movie takes place in the 40s or 50s, but there are several modern buildings in the background.
Continuity mistake: Dickie's extra lover, Silvana, turns up dead, during a religious ceremony, and before anyone can get to her, she is face down, but when they do get to her, she is face up, without anyone touching her or from choppy water - the water is flat, no chop.
Continuity mistake: When Sylvana's body is found during the "Festival of the Madonna," her body floats up on its stomach; there are no waves and she is in fact dead, so how then does her body get from her floating on its stomach to floating on its back in one shot?
Continuity mistake: When Dickie and Tom go out on the boat, Dickie is wearing his white jacket. When Tom swims back to shore, the white jacket is dry on the rocks as if Dickie hadn't taken it with him.
Continuity mistake: When Tom is with Peter on the boat sailing to Greece and Tom says he's going to watch the sunset, the sun is just above the horizon. When Tom goes into Peter's room after talking with Marge, you can see the sun in the exact same position out the porthole window in Peter's room.
Continuity mistake: From the viewpoint of a boat behind Dickie's boat "The Bird", when Dickie gives the tiller to Freddie, so he can go below with Marge, there's hardly any wind, both sails are flapping around, but when we get the view from midships, the front sail, which was on the starboard side, is now, suddenly, on the port side and full of wind, no flapping around at all.
Chosen answer: Tom & his lover are travelling on a boat. The rich girl, who knows Tom as Dickie is also on the boat. If they were to meet, Tom's false identity would have been revealed, and the lover would have been able to figure out that Tom actually murdered Dickie.
marfbody