At the end of the movie, when they are driving off to go on their date, right before the secret service turns the corner. At the four way stop, drivers are supposed to stop, but Duncan didn't stop at the stop sign.
At the end of the movie, when Duncan and Hallie are going out for a second date, the camera pull back to show Secret Service SUVs and a helicopter following Duncan's car. The buildings are skyscrapers, which are much too tall to be Washington DC, as building codes for the District provide that no building may be taller than the Capitol, which is only 287.5 feet tall. (The Washington Monument is the only exception.)
When Duncan is asking his dad if he can take the car, his dad tells him to take the station wagon, and hands him a ring with only one key on it. Duncan takes the company car, but both cars wouldn't use the same key.
When the President and Duncan's dad are in the mall looking for them, they say "There they are!" pointing at a couple wearing the same thing Duncan and Hallie are wearing. But, the President and Duncan's dad never saw them wearing their new clothes.