The car has a rearview mirror when Goldie rescues Tom from the police. It is gone as they drive around the block, but is back when they return to the hotel.
The cars of the express train on which The Falcon and Goldie are traveling are obviously studio mock-ups as they show no train movement whatsoever with passengers and staff having no trouble standing or walking in the corridors.
For some reason, some shots of the streamlined Pennsylvania Railroad locomotive are reversed, as evidenced by the numbers on the side and the logo on the front of the locomotive, and the word "Pennsylvania" on the tender behind.