The Association of Catholic Priests, an unofficial grassroots group of Irish clergy, met in Dublin yesterday to call for reform of the Church, specifically married priests, the ordination of women and the election of bishops.
A married clergy is not impossible but unlikely with the current Pope. The Eastern Catholic churches have married priests and there have also been papal dispensations for married Anglican clergy opposed to women's ordination to become Catholic priests in the last decade. The ordination of women is much harder to imagine given the theological questions it would open up, not least among the ex-Anglican priests who have joined the Church over this very issue.
It is the election of bishops though that really is a bridge too far for the Vatican. The Catholic Church has been accurately described as a fragment of the bureaucracy of the late Roman empire that has floated down through the centuries intact. It's not clear who would elect bishops - clergy? laity? - but whoever it was it would subvert the whole basis of the Catholic Church. The Church teaches that the Pope, as the bishop of Rome, is, like his predeceesor the Roman Emperor, divinley appointed. The conclave of cardinals that elects a Pope is believed to be guided by the Holy Spirit to choose the right man who then becomes Christ's representative on Earth.
Although I am impressed by the courage of the Irish priests challenging the Vatican, they will surely discover, as Martin Luther did five hundred years ago, the impossibilty of attempting to reform the Catholic Church from the inside.