Continuity mistake: During the scene where he is first at the cave, look in the sky. First, there aren't any clouds then there are in the next scene. If you keep watching, the clouds vary from the different camera angles.
Continuity mistake: When Tom Hanks is on the plane he sets down the pocket watch in the lower right corner of the groove in the seat, after an instant angle change it is closer to the upper left corner of the groove, with no time for it to move. (00:20:25)
Continuity mistake: At the Christmas meal, Chuck gets passed the candied yams. When he takes the yams, there is a spoon in the dish. When the shot changes to behind him, the spoon is not in his hand. (00:14:30)
Continuity mistake: When Tom Hanks sees the ship from the beach, it is obvious there is a pane in front of the camera. However, as he is jumping up and down through the scene, his shadow changes angles from in front of him, to a very low angle behind him.
Answer: Cast Away was filmed on an island called Monuriki. It's part of a group of islands called the Mamanuca Islands, in Fiji.