In 1997, baseball commissioner Bud Selig universally retired Jackie Robinson's number, 42. The handful of players still wearing the number were allowed to keep it. As of 2014, barring special requests or approval, no major league player will wear #42 again.
Pee Wee Reese's line that someday all Dodger players might be wearing the number 42 was actually said by Dodgers outfielder Gene Hermanski in 1951. Brian Helgeland liked the quote so much, he had Reese say it because he is a central character. Since 2004, every April 15th has been "Jackie Robinson Day" in Major League baseball, and every player wears number 42. Robinson's first day in the Major Leagues was April 15, 1947.
The line "No. I want a player who's got the guts *not* to fight back." was actually said by Branch Rickey to Jackie Robinson.
Four players from the 1947 Brooklyn Dodgers were still alive when this film came out: Tommy Brown, Ralph Branca, Marv Rackley, and Don Lund.
The film does not explore Jackie Robinson's career with the Montreal Royals, but he was hugely popular. After leading the team to the league championship, it was noted: ..."probably the only day in history that a black man ran from a white mob that had love, not lynching, on its mind."