The part of Special Assistant to the President Jack Valenti was played by his son, John Valenti, in the latter's first acting role. Jack Valenti later headed the Motion Picture Association of America for 38 years.
The interiors for Vietnam, especially "the hospital" is actually the old Camarillo State Hospital, which fell victim to Govenor (and subsequently President) Reagan's budget cuts, which abandoned mental health care in California, precipitating "the current homeless" situation, especially in California!
The grounds presently house part of CSCI (California State Chanell Islands).
John Frankenheimer was a close friend of Lyndon Johnson's political rival Bobby Kennedy (having even driven Kennedy to the Ambassador hotel the night he was assassinated). Frankenheimer admitted that his view of Johnson was negative at the time, but he gradually came to have a more sympathetic perspective and that was his motivation for making the film.
Gary Sinise: Gov. George Wallace. He previously played Wallace in George Wallace (1997), also directed by John Frankenheimer. The footage of Wallace on television is from Sinise's performance in that film. In the scene right after he is also shown taking a publicity shot with LBJ, then talking to LBJ then ending with a press conference.
The trivia item below may give away important plot points.
When President Johnson is convincing George Wallace to follow his idea on ending segregation laws on his state, Johnson urges the other one to imagine what his legacy would be in the following years, long before they're dead - which he says that by 1995 they both would gone. However, in reality, Wallace managed to live after 1995 (died in 1998) and a changed man.