The end (midnight) town square gathering was actually shot at 1am. The crew had to wait for the local high school band to arrive. The band had a football game to play in and they held up shooting for some time, because they were late to get to the set.
The Christopher Mott Society is a parody of the ultra-right-wing John Birch Society. In the scene where the Mott society is meeting, they listen to a record album of a talk by a right-wing pundit; many right-wing pundits put out albums of their speeches in the 1960s and 1970s and widely distributed them for sale in friendly newspapers, since they could only afford to get radio time on low-power stations.
Dropping the cigarettes onto the crowd, in the last midnight town square gathering, was actually done by putting 8" diameter, 25'-long pipes against the trees in the town square. The pipes were then filled with cigarettes. Then, on cue, air was blasted into the pipe bottom, shooting them into the air and onto the crowd. After each take everyone was asked to gather up the cigarettes from the ground and turn them in so they could be reloaded into the cigarette canons and rained down again. The filming of this final scene took several weeks in the late fall in Iowa where it is pretty cold. In the movie it is supposed to be summer time so the actresses are dressed in summer dresses. In between takes everyone (actors and extras) were huddled in winter coats sucking on ice cubes. The ice cubes kept their mouth and breath cold so they wouldn't steam when they breathed.
In the opening scene where Merwin Wren is talking to Hiram C. Grayson, a banjo can be heard playing Elmer Bernstein's theme music from The Magnificent Seven (1960). The tune was known for its use in television commercials for Marlboro cigarettes in the 1960s.
During the off days of filming, in Iowa, Dick Van Dyke rented a car to drive around the open spaces and small towns locally. He ran out of gas one day, and sat on the roof of his car whistling by putting a blade of grass up to his teeth and blowing. A farmer happened by and gave Van Dyke a lift to get gas.