The flashback to Robert Duvall's character failing to save his wife from a burning house was shot north of Brule, Nebraska, with the help of the local volunteer fire department. Duvall's wife is played by director Francis Ford Coppola's wife, Eleanor Coppola (uncredited).
Much of this film was shot in and around Ogallala, Nebraska. Some landmarks visible in this film remain in the area, especially Front Street, a tourist attraction visible behind Shirley Knight as she stands in the phone booth. (That phone booth was removed in the 1990s.)
The parade scene was filmed in Chattanooga TN on Veterans' Day. The students in the band were not aware of what was happening. In fact , you can read the lips of a majorette asking "Who was that guy?" As James Caan was weaving through the parade. My husband was the drum major and has a full shot and never knew it until someone told him years later.
George Lucas visited the set while finishing film school, having heard that Francis Ford Coppola, a fellow film school graduate, was directing. The two struck up a fast friendship and became frequent collaborators during the 1970s.