Although I agree with #7's point -- that national competition led to innovation -- I also think that the weakening of the Church had a great deal of influence as well. Before the Great Schism, the Church led and controlled most areas of commerce and business, both directly and indirectly, and had a history of suppressing thought and action that would move against them, or even cut into their power. As the Church lost influence, people were more able to freely exercise their own innovation and entrepreneurial spirits.
Are you speaking of the Great Schism of 1054 or of the Great Western Schism of 1378? The Great Schism of 1054 led to the origination of the Western Roman Catholic (i.e., universal) Church and the opposing Eastern Orthodox Church. The Great Western Schism of 1378, on the other hand, occurred within the Western Roman Catholic Church. Basically, The French would not accept Urban as Pope and appointed Clement, based in Avignon, as the rightful Pope. The Western countries were torn about whom to obey as Pope of Christendom. Depending upon which Schism you are speaking of, the affects on the advance of Europe would be quite different. In the Schism of 1054, the greatest affect might be to cause people to hold more tightly to old forms as the rupture was essentially over the validity of forms of orthodox worship. In the Schism of 1378, the greatest affect might be to turn to new ideas since the established ones were crumbling in animosity around adherents.
I disagree with many of the answers here. The weakening of the church in the Middle Ages did not bring about development. If anything, the Great Schism caused there to be more nationalism. This, in turn, caused greater competition among nations and it was this competition that lead to greater growth and innovation.
It also contributed to movements within the Church that promoted a more spiritual version of Christianity-the first Pietist movements in Germany, for example. It also led to the Conciliar movement, which (in theory, at least) limited the power of the Pope by giving some power to regularly summoned councils. And, of course, it contributed to the power of kings by weakening the papacy.
By weakening the Catholic church and by exposing the church's flaws, the schism allowed other centers of power to arise. The schism also helped promote, eventually, the rise of Protestantism. The rise of Protestantism has in turn been associated with the rise of science and with a commitment to a strong work ethic.
I think #2, as normal, makes a very valid point. The role of the Great Schism in exposing the duplicity and hypocrisy and corrupt nature of the church was key in liberating national powers and individuals to assert themselves and follow their own agenda rather than being dicatated to by the Papacy.
Any time an organization is fighting within itself, it becomes weaker. This allows people to see inside the veil, as post 2 mentions, and also paves the way for other people to take power, and for followers to change their allegiance.
If it actually did help, it would have to be by weakening the Church and the respect that people had for it. The Great Schism made the Church look very corrupt. This weakened the Church greatly. As the Church became weaker, its hold on the political and economic lives of the people weakened as well. This allowed for a freer society that was able to become more innovative in its thought and in its economic system.
In the process of the Great Schism between 1378 and 1415, the Church was converted from a religious institution to a political platform, contesting the Roman Catholic Church and the Avignon Papacy. The masses lost faith in religion over time as both papacies were more occupied electing more cardinals to their side to legitamise their stand for being the true leaders of Catholicism over spreading the gospel and helping the masses understand the gospel better.
As discontent with both Papacies arose, the Holy Roman Empire, in the form of the Council of Constance, managed to depose or force all three Popes to resign (the third being elected by the Council of Pisa). Although Martin V was established as the new Pope, the CHurch grappled with problems such as religious heresy and failed attempts for internal reform. Since then, the Church's credibiltiy as the leading religious organisation for Christianity was tarnished for prioritising political agendas over religious ones. THe Great Schism woud later contribute to Martin Luther's Protestant Reformation.