The scene where Savannah tells the story of Brer Rabbit to Bootsie and Alvie was not originally in the script. In Bridgette Andersen's screen test they asked her to tell them a bedtime story and they were so impressed with her performance they added it to the film.
[Source: her uncle, Steven B. Andersen from the Bridgette Andersen Facebook memorial page. He has posted some rare photos of her so he appears to be credible. Mark Miller who wrote the screenplay and starred in the movie confirms this in an interview recently posted here.]
Mark Miller originally wrote this screenplay intending that his daughter Savannah play the starring role, but by the time it went into production she was too old for the part. She did have a small role as Savannah's cousin Beth. His daughter Marisa Miller also has a minor role as a jogger, and his wife Barbara Stanger played Savannah's mother.
At the end of the scene where Alvie and Boots steal groceries from a grocery store, they run out of the store and into a car, dropping some of their groceries as they run. A cantaloupe roll down the driveway and get scooped up into the side of the front bumper. Just a case of perfect timing.
The Texas flag flying over the work area at the beginning of the movie is upside-down.
In the scene where Alvie and Boots are robbing the grocery store, Donovan Scott (Boots) has some unexpected "fun" with a cantaloupe. While throwing produce at the grocery clerk, Boots intended to bounce the cantaloupe off the clerk's head, but what happened next was not intended. The cantaloupe bounced off the head of John Fiedler (grocery clerk) and accidentally back into the hands of Scott as he turned to run to the getaway car. Scott then turned back and threw the same spherical fruit at Fiedler a second time. The cantaloupe then rolled into the road and got stuck in the bumper of the getaway car. It was one of those fortuitous moments for which movie producers could never plan but are thrilled to catch on camera.