Pope John Paul II did wonders in confronting the many divides within the Catholic Church and between that church body and the rest of Christendom. There remains much, much work to be done, of course, but I believe that the beginning he has made (which of course builds on earlier reforms which, ironically, many American Catholics strongly opposed and still do) will leave a lasting legacy if the church continues to build on his accomplishments.
In my view, the greatest source of this pope's success—beyond his hard work, passion, and wisdom—was his willingness to question all things while remaining true to the essentials of his faith and his church. That is a perspective the Catholic Church and its next leader must retain if progress is to continue.
The church must continue to ask serious questions about its internal organization and its engagement with the world. The answers will greatly displease many people. Nonetheless, fulfilling its mission, the Great Commission, must be the central consideration in all church matters. Where traditions or current doctrines and practices stand in the way, they must be abolished. Where these things serve the misson of the church, they should be strengthened.
Ultimately, the aim of the Catholic Church is to be catholic, to be universal among all Christians, which it is at present very far from becoming. However, as Hunter Baker has pointed out on this site and in writings published elsewhere, the major orthodox Christian groups are closer to one another than at any time in centuries. (I should also add that the Christian church may now be in closer harmony with believing Jews than it has ever been.) Appropriate internal reforms combined with principled ecumenicism should be the goal of all Christian churches, and it is right that the world's largest Christian church body should lead the way.
In this endeavor, all Christians should wish for God's great blessings on the Catholic Church.