Openness (Transparency). This is pretty self-explanatory, and it is something the Church should choose to do voluntarily. Too much of what the Church does is kept secret, hidden from the flock and closed off from the public. If people believe the Church is imbued with the Holy Spirit, then why would openness be a problem? The truth and God are supposed to be one, so transparency should always be the first inclination. Much of the fallout from recent scandals comes from the darkness of secrets kept. Turn the lights on, and let the chips fall where they may. The first thing the next Pope should do is open all the files, open all the doors, and let the fresh air of truth sweep through the Church.
Simplicity. Again, another value not needing much explanation. It is time the Church in its outward manifestation return to a more simple time. The next Pope should strip Rome and every Church around the world of all the extravagant tastes and possessions built up. Sell off the gold and silver and jeweled possessions. Give away those things and all possessions not central to the mission of the Church. Strip away those expensive manifestations, and begin to teach the flock that the only way to the Kingdom of God is not through retail therapy, but a life of simplicity and non-attachment to material things.
Passion. Many folks see this value as in conflict with the Church. It is not. Without passion, the Church becomes stale and withered like an old book in the recesses of a library. Passion allows us to fight injustice. It gives us the courage to do the right thing. It causes us to believe we can make a difference and we matter. For too long the Vatican has been an institution of the head, extolling rational sermons and reasoned promulgations. The Vatican must become more of an institution of the heart. The next Pope should be heart centered, not head centered. It is through heart connections or gut connections that institutions can link with today's flock. If you capture folks' hearts through a connection based in love, then you have an enthusiastic and passionate Church.
Diversity. This may be the toughest one for the Church, which seems to keep coming up with theological reasons why there can't be more involvement by the laity and a more diverse leadership. If the next Pope wants the Church to grow and thrive and matter to today's world, then it must figure a way to broaden the role of women, youth, and the laity as a whole. In many churches around the world, there is laity sitting in the pews that could give much better sermons than existing priests. Why shouldn't we ask about the possibility of married priest, or women priests? And without outreach to today's youth, then the Church is destined to die of just looking at demographics. The next Pope should quickly call a series of conclaves or conferences addressing women, youth, and laity, and their role going forward. This would be a huge step forward.
Those are my thoughts. I hope as the Cardinals gather they spend some time thinking through how to be a vibrant and growing and connected Church around the world. The world needs it. Pax vobiscum.