At the engagement party Faith's fiancé is boasting a little about his knowledge of diamonds: he says it is amazing how many varieties of pure carbon there are crystallized as octahedrons. Actually there are no such varieties: the structure of diamond is not octahedral but tetrahedral.
When Damon and Faith finally meet, they make plans to meet at the restaurant at 8:30. When she runs down the stairs to meet him, we hear a bell tower chiming multiple times. Presumably, it is either 8:00 or 9:00.
At the very end of the movie, the plane shown is an Airbus A300. On take-off, it becomes a Boeing 727 in silhouette.
At the beginning of the movie, Faith writes down the name "Damon Bradley" on two lines. In the next shot she writes the name down on one line.
There are obvious stand-ins for Marisa Tomei and Robert Downey, Jr., in two shots during the Ferrari car ride from Rome to Positani.
When Faith and Kate on their way to Rome are having lunch beside the street, they drink white wine out of a bottle labelled as Chianti. In Tuscany only red wines can be labelled as Chianti.
When Faith first arrives at the airport, she goes to the departure board to look for the gate for Damon's flight to Italy. She points at one and nods her head as if seeing it, then continues on to the gate. However, there are no flights listed to any destination in or near Italy.
Right before we see Faith packing her case at La Sirenuse, there's a shot of what is supposed, in the film, to be sunrise. However, given the geography of Positano, the position of the sun in that scene means it's actually sunset.
When Kate is running with Faith to get on the plane to Italy, Kate says, "I wish I had my passport"... but she gets on the plane anyway.