Jack Webb actually knew how to play the cornet. He loved jazz music and, as a boy, was given a cornet by a musician who lived near his home. While he never truly mastered the instrument he knew it well enough that his handling and fingering of the cornet in this movie is accurate.
"Pete Kelly's Blues" was originally a radio series created by Richard L. Breen and starring Jack Webb. It ran on NBC as a summer replacement series from July 4 to September 19, 1951. It later became a short-lived TV series (Pete Kelly's Blues (1959)), produced by Webb.
The release date above lists 31 July 1955, yet in a special episode of "Colgate Variety Hour" (24 July 1955) devoted to this film, Jack Webb emphasizes, complete with a written out sign, the date August 1, 1955 is the big day.