During the scene in the Texas airport, Dean Stockwell's character is on the phone with his wife. The PA announcer can be heard saying "A message for Joy Stockwell, Joy Stockwell. Austin will arrive at any minute." Joy was Dean's wife and Austin, his son, was born during production of this film.
The restaurant that Travis calls Walt's home from is actually located in Cabazon, CA (not San Bernardino, which is about 45 miles away.) This of course is home to Claude Bell's famous concrete T-Rex and brontosaurus.
Shooting started in 1983 while the screenplay was still incomplete, with the objective of filming in the order of the story. Writer Sam Shepard planned to base the rest of the story on their understanding of the characters and observations of the actors. However, when Shepard moved on to another job, he sent director Wim Wenders notes on how the screenplay should end instead. He credited Wenders and co-writer L.M. Kit Carson with the idea of a peep show and the story's final acts. According to Dean Stockwell, his character in early drafts was intended to travel with Hunter, Travis and Anne before Anne turned back to Los Angeles and Walt became lost in the desert, paralleling Travis in the first scene.