Paul Newman was concerned about his accent, so he spent two weeks in Mexico with dialect coach Walon Green.
Paul Newman wore a prosthetic nose for his character, and MGM shipped two of them each day to the filming location.
Paul Newman opposed sound looping the picture, stating it interfered with the actors' performances, so a small (for that time) chest microphone was developed that eliminated around eighty percent of dialog looping, and saved its associated post-production costs as well.
This was one of the first films to put all the credits at the end rather than at the beginning. It's a practice that would become standard by the 1970s, but in 1964 it was extremely unusual.