In the restaurant, when the waitress is putting the food onto the table, there is much greenery on Oliver's dish. But in the shot from behind Oliver's shoulder there is almost no green.
At the Japanese restaurant, the amount of water in their glasses changes very drastically several times between shots.
In the Chinese restaurant scene, the girl gets her food and it appears to be a full plate. The camera cuts away and then back to her and seconds later the food is nearly gone.
In the beginning of the movie, when Emily visits the churchyard, the trees indicate that it is summer. In the next scene, when she and Oliver walk in New York, it is autumn/winter. Additionally, the establishing shot leading to the churchyard scene shows the trees to be bare, but the surrounding trees in the shot where Emily walks toward her mom's grave are in full bloom.
After leaving the airport, Emily and Oliver are on the train platform. As they're talking, Emily lights a cigarette, takes a few puffs and then drops it and stamps it out. In the next scene she takes another drag on a cigarette without lighting up another, and drops this one and stamps it out.
The nude photograph in the desert. Emily sets the shutter at 40 seconds (the time they need to remain absolutely still) but with such a long exposure the moon and stars would move enough to get all blurred as well (a lot less than one second is required). When we later see the photo the moon is sharp.
When Oliver and Emily are in the bar in New York, Oliver pays with what appears to be two bills that are of the "new style" (larger head shots of the presidents, etc.) although the scene is supposed to take place before this new monetary style was introduced.