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.
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.