Harrison Ford damaged some ligaments in his leg during the filming of the scenes in the woods. He refused to take surgery until the end of filming so that his character would keep the limp. The limp can be seen in any subsequent scene where Richard Kimble is running.
The scene where Kimble is running through the St. Patrick's Day parade was not scripted. This was a later addition by Andrew Davis. Davis, a native of the city, really wanted to capture the parade and was granted permission from the mayor's office to film the day of the parade. The entire sequence was shot with a hand-held steady cam. Without rehearsal, Ford and Jones just went out into the crowd and did their thing, with camera operators running around trying to keep up. Ford observed that since his character was keeping a low profile, it meant he himself didn't stand out much and lasted several minutes in the crowd before being recognized.
According to director Andrew Davis, Tommy Lee Jones briefly held up filming when he objected to Gerard shooting at Kimble in the courthouse, arguing Gerard would not risk endangering civilians in a crowded building. Davis eventually convinced Jones to do it as scripted.
According to producer Roy Huggins, Gerard's line in response to Richard Kimble's claim of innocence ("I didn't kill my wife") was originally written as "That isn't my problem." At the request of Tommy Lee Jones, it was changed to "I don't care."
Originally, Julianne Moore's character had a bigger role in the film, even after she exposes him briefly. Kimble was to have sought her out for help and eventually fall for her. These scenes were filmed and deleted from the final cut of the film. This is the reason that her name is still credited as one of the main stars of the picture.