Continuity mistake: Just after Gatsby asks Nick his opinion of him, there is a cut to a low angle of him driving. In the shot from behind the car, the number plate is on the right hand side of the back of the car. This is only visible for a fraction of a second, so you have to be quick when you look at this. 2 shots later, the number plate has moved to the left side of the back of the car.
Picture added by Casual Person