It was an accident when Ashton Kutcher was hit by the "10 pound" ash tray by bouncing off a prop. He recovered but with a large goose egg for about a week.
Before filming the scene with the car buried in the snow, Brittany Murphy and Ashton Kutcher had an argument which helped them get through the scene without breaking out into laughter.
When Tom and Sarah are on the plane (going to Europe), the tissues in Tom's nose change size and/or shape (particularly the one in his left nostril) between shots.