River Phoenix's marine haircut (called a "high-and-tight") was deemed so unflattering that Warner Bros. requested highlights be added to Phoenix's hair to soften the young actor's appearance.
The first and last scenes (River Phoenix on the bus and then River and Rose reuniting) were both shot the first day of filming. River was upset about this unusual way of movie making because he had to shoot the last scene before making the whole movie.
Right after Birdlace sticks the note to Rose's window, he loses his balance and falls, however in the next shot, as he is jumping over the fence to avoid Rose's attack dog, the window is empty and the note is nowhere to be seen.
Through the rear window of a bus can be seen a "do not enter" traffic sign (red circle with a white bar). European style traffic signs were not approved for use in the U.S. until the late 1960s and installations began in the 1970s.