About ten minutes into the movie, Chance Wayne checks into a hotel and his coat is half way on. He then puts it on and the collar is not straight. In the next shot from behind his collar is straight. The next shot shows him walking away and his collar is again slightly crooked.
During the pot-smoking scene, there is one shot in which Chance is seen looking to his right with the cigarette in his mouth. We cut to another angle as Alexandra flops down on the bed, and now Chance has no cigarette and his head is leaned straight back on the mattress.
Just after the opening scene in which he and the Ms. Page character are leaving Florida, the Paul Newman character pulls their Cadillac off the road and parks it in front of a liquor store, where he goes in to get Ms. Page's character a bottle of Smirnoff vodka. Look carefully at the neon signs in the liquor store display window. One of them clearly advertises Coors beer. But this is supposed to be the eastern United States (presumably a Gulf Coast state), and Coors was only sold in Colorado and western states at that time.
In the beginning of the movie as Chance is driving, he sees a sign saying "You Are Now Leaving Florida." The multi-lane highway runs very close to the beach with no buildings in between the road and beach and dozens of oil pumps adjacent to the highway. This was clearly filmed in southern California.
The film is set in the Gulf coast town of "St. Cloud," which is the name of an actual inland town in central Florida. However, Chance and the Princess are shown driving out of Florida at the beginning of the film, so the movie is not set in that state. It seems most likely that "St. Cloud" is a fictional town, intended to stand in for a coastal location in Mississippi or Louisiana.