Other mistake: When Neal checks his airline ticket it says he departs from N.Y.C. J.F.K. but the movie claims to have him flying out of LaGuardia.
Other mistake: To go from Wichita, KS, to Chicago, they would go NE through KS, Missouri, Illinois. Kentucky is NOT on the route. They are pulled over by Kentucky State Police (Lenny). But this is the trip from Hell. Maybe they took the L O N G way East to Paducah, then back North to Chicago.
Answer: He had multiple cards. He shows the burnt remains when he tries to rent a room.
Brian Katcher