Continuity mistake: When Tom, as Dickie, rents a place in Rome, and after Tom kills Freddie, the police are all over him. Marge comes calling and Tom, as Dickie, asks the policeman to ask her to come back later, which leaves Tom alone with the detective. But as we see Marge creeping up the stairs, to see Dickie, suddenly, the policeman is with Tom and the detective, even though the policeman had left and Tom had closed the doors, so the policeman should not have been there.
Continuity mistake: When Marge gets out of the water and climbs the stairs on the sailboat her swimsuit is blue. But when she is on board and we get a close up it is red.
Continuity mistake: When Freddie is driving the boat, the direction keeps changing from shots to shots. Dickie told him to keep the same direction.
Continuity mistake: During the opera intermission scene, when Tom first meets up with Marge and Peter, Peter's hair is neatly slicked back. In the next shot, his hair is hanging in his face a little. The next time he's shown, his hair is neat once more, and a moment later it's messy again.
Continuity mistake: When Tom and Dickie enter the jazz club in Naples, Dickie's hat keeps appearing and disappearing from his head. (Within the film this is a matter of continuity and thus a mistake, regardless if there is an explanation on the music video.)
Continuity mistake: A far ways into the film, when Gweneth Paltrow is leaving on the boat, Matt Damon is standing on the dock watching her leave. At one point, it cuts to a far shot showing him pulling his hair back with his hand, but then it shows a shot from behind, and his hands are down at his sides. It's not very likely he could move his hands that fast.
Continuity mistake: In the scene where Tom is analysing Dickie's handwriting, Tom is smoking a cigarette and is shown taking a puff. The camera suddenly cuts to behind Tom's head where he has moved his arm & the cigarette - there is not enough time for him to do so. (00:28:24)
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: You can see the red in the water on the left side of the boat. This was before Ripley murdered Dickie. (00:53:14)
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: When Tom is taking Freddy's body out of his building, Freddy's coat is buttoned to the top. When Tom puts Freddy in the car, his coat is suddenly undone and blood is visible on his shirt. (01:28:00)
Continuity mistake: When Tom is playing the piano in the apartment, he has both of Dickie's rings on, but when he gets to the door when Freddie is there, he only has the pinky ring on the left hand. The gold middle finger ring is now missing when ne puts his right hand up on the door, but he never took it off. (01:21:00)
Continuity mistake: Tom has a scrape on his face as he is typing the "suicide" note in the apartment. But as he is leaving and peering around the corner of the building, the scrape is gone. (01:38:00 - 01:44:00)
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.
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.