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.
In the scene where Oliver and Emily are sitting at the bar, Oliver asks the bartender to make their second round a double. The bartender remarks that the shots they are drinking are doubles even though they are clearly drinking out of standard 1.5 ounce shot glasses.
When Oliver has just lost his job and is seen leaving a store with a gray sweater on, a black female extra talking on a cell phone walks past him. Five seconds later the same extra still talking on the phone walks past him again in the same direction.
During the New Year's Eve party, the location of the large tattoo on the back of Emily's left shoulder changes position by at least a few inches from shot to shot while she's sitting facing the bar and later when she's dancing with Oliver.
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.
After Oliver and Emily walk out of the restaurant after Emily is upset, they drive off. The shot shows a Toyota Corolla in front that is not giving way and Emily is frustrated by the driver. Oliver asks her to take it easy before Emily overtakes the car. The overtaken car is now a Ford.
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 then one second is required). When we later see the photo the moon is sharp.