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.
On the "subway" train, the man holding the USA Today paper is Cameron Crowe, and the woman in the seat behind him on his left is Cameron Diaz. Because "Vanilla Sky" and "Minority Report" were so close in shooting, the two directors (Crowe and Spielberg) agreed to put themselves as cameos in each other's films.