In the car chase at the end of the film, the position of the taxi sign on the windshield of the car Harold is driving changes between long and close-up shots.
Harold spins a globe to choose where he takes Larry for a rest. Although they fly to Baja, Mexico, his finger actually landed much further north on the globe, probably somewhere between Juneau and Anchorage, Alaska.
The flight from New York to Caliente is graphically depicted as a single, direct flight. In reality, there would have been at least two stops along the way. Nonstop transcontinental passenger service did not begin until after WWII.
The film is flipped when they arrive in Caliente; the "Stop" sign and "La Internacional" on the building are backward.