In the beginning, when Anderton arrests the jealous husband, he notes that he is being arrested on April 22 - that day - for the future murder of his wife and her lover. Later, while Anderton is jogging, we see billboards advocating a "Yes" vote on pre-crime on April 22. The next day, Anderton's boss Lamar notes that the vote is in a week, which would make it April 15, making the day that the jealous husband was arrested April 14, not April 22.
Paul Thomas Anderson, who directed Tom Cruise in Magnolia, has a cameo on the train. It is reported that he is so hard to find that Anderson himself does not know where he appears.