The letter Vincent wrote to Olivia in his car is in different handwriting than the one shown later near the end of the film.
In the opening bedroom scene, the "iconic" clock shows a few minutes before 8:00, then immediately zooms in for a closeup that shows the time has changed to 8:15.
After the little girl gives Vincent something to eat she gets in her grandfather's truck and only partially closes the door. As the truck pulls out in the next shot the door is properly shut.
When Vincent washes his face after arriving at the diner he looks wistfully at his reflection in the bathroom mirror. A member of the crew is visible behind him.
After the "Tale of Two Cities" scene, Vincent is driving on the highway when a white object flies off the camera truck and lands in the opposite lane, just missing his car.