The background shows the colorful canyon country of the American southwest, including what appears to be a glimpse of Monument Valley, as well as Saguaro cactus, yucca, agave, and the Joshua tree.
The slingshot gag was used in this cartoon alongside other slingshot gags from two other Road Runner Cartoons, "Guided Muscle" and "Wild About Hurry" were used in The Bugs Bunny Road-Runner Movie.
The first of the so-called "gray sky" Road Runner cartoons; this color choice would continue until Gee Whiz-z-z-z-z-z-z (1956).
Both characters appear in drag during the action.
The DSC on Coyote's transport likely refers to Department of Street Cleaning. The bucket type device was used in ages past, when street sweepers were actual people with push brooms. They can often be seen In older films and TV shows, too.