What dispute between Byzantines and the pope lead to?

Answer 1

Eventually, it led to the Schism of the East in the 11th century. This from the website "The Byzantine period"

In the eighth century a controversy broke out between the Byzantine emperor Leo III and the pope concerning the use of icons or images in church worship, the emperor taking the position that the icons were an aid only to superstition while the pope claimed that they heightened religious feeling. When Leo and his successors forbade the use of images and ordered them to be broken, the pope was powerless to do more than protest; but the Iconoclastic Controversy embittered relations between Rome and Constantinople for a century, and undoubtedly contributed to the desire of the popes to be protected by the Franks rather than by the Byzantine emperors, who were in their own view little better than heretics. The controversy was at last settled in favor of the papal position in the ninth century. But only twenty-four years later a further schism developed between the two Churches, and a Church council dominated by the Byzantines anathematized the pope and rejected papal supremacy (867). Though this quarrel too was patched up, Greek national feeling became involved, and the pretensions of Rome became ever more abhorrent to the Byzantines. Finally in 1054 the split became permanent, ostensibly on a question of doctrine-though the competing interests of pope and patriarch in southern Italy, which had just been conquered by the Normans, were perhaps more important at the time. The Orthodox and Roman branches of the Church have diverged on doctrine ever since.