Revealing mistake: When the main characters get off the liner, you can see the set wall in the background. (01:02:31)
Visible crew/equipment: On the porch, behind the woman is a boom of some type. (01:09:47)
Other mistake: When Cary Grant came to visit Deborah Kerr, he laid his coat and hat in the chair. Later he remembered he had a gift from his grandmother for her. He did not have it when he came in. Someone had to put it under his coat.
Revealing mistake: An open water shot of the Constitution shows the wake from the camera boat.
Character mistake: When Cary Grant enters Deborah Kerr's apartment he greets her by saying, "Hello Debbie." Kerr is Terry.
Suggested correction: He says "Hi, Terry", calling her by the right name.
Factual error: They stopped off at a European port after at least a few days after leaving, presumably, Southampton UK. Perhaps they embarked in Holland or Germany but that voyage to a French port would not have taken days on the open sea.