Factual error: A copy of Miles Davis' album "Tutu" is sitting on a counter. Odd since the recording wasn't made until 1986.
Factual error: When Dickie and Ripley go to the first jazzclub together and Dickie and the Italian singer invites Ripley to join them on stage, the microphone they're using is entirely misplaced. That type of microphone wasn't even on the market yet.
Factual error: In the scene in Venice where Marge is leaving on the boat with Dickie's father, there is a shot from Tom's point of view looking out onto the water. In the distance a modern crane can be seen on the left - something that the director Mingella himself points out on the DVD commentary. (02:00:00)
Factual error: The ship on which Tom sails from Venice to Athens is shown from above at sunset. The sun is to the front left of the ship. That means that the ship must have been sailing West, which is hard (and weird) to do on that route.
Factual error: The scene where they are in the cockpit of the sailboat shows StayLock rigging, which was not invented until the 80s.
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.
Answer: After running into Meredith, Tom's plan was to stay in the cabin with Peter the entire trip to avoid them seeing one another. But after Tom makes that suggestion, Peter tells Tom that he seen him kissing Meredith. He couldn't avoid or kill her since Peter already saw her. Family members also saw Tom with Meredith. If Meredith suddenly vanished or was killed I'm quite sure there'd be an investigation. Peter was the only option. No one is on board to report Peter missing. Once the boat docks, Tom will be long gone before they discover Peters body. Unlike Meredith, her family would be looking for her immediately since they're traveling together. I'm quite sure he'd much rather have killed Meredith, she meant nothing to him.