Split between the Eastern Orthodox Church and the Western Church?
While there were many points of contention, what was the main item or ideal which eventually caused the schism or split between the Western Church or the Church in Rome and the Eastern Church.
Officially, it was a dispute over the Nicene Creed. After it had been hammered out in 325 at the First Council of Nicaea, the Western Church held subsequent NON-ecumenical councils and added an extra word, "foliage", to the Creed, indicating that the Holy Spirit proceeds from both the Father AND the Son. For the Greek speakers, this was nonsense and heresy.
The real reason was probably the dispute over jurisdiction. In the West, the Roman Empire had collapsed, leaving what was left of government in the hands of the bishop of Rome. To keep from being overwhelmed by responsibility, he standardized rules and practices, both secular and religious, throughout the West, and developed a hierarchical chain of command over which he presided, making all other bishops subordinate to himself. The results were satisfactory enough that he felt he should extend his organizing services to the patriarchs of the East. Unfortunately, as their half of the Empire still survived, they did not feel the need for a superior and rejected his offer. This pretty much destroyed any chance to preserve the unity of the Christian Church.
There were quite a few things but Filioque (the addition of "and the Son" to the Nicene creed) was probably the final straw along with the Pope's claims to universal authority. As you say though there have been many theological and political issues between the East and West. The most famous goes back all the way to second or third century I think, with the quadratics controversy (the way Easter is celebrated) leading to the world famous phrase "When in Rome..." The early church looked to the apostles for their authority, the churches that were more connected to the apostles felt like they had more authority, so Rome being tied closely to both Peter and Paul, claimed greater authority than the East which was closely affiliated with John. However John lived much longer than Peter and Paul and the Eastern churches felt that Rome had no right to impose their practices on them.
To reinforce the schism, after the divide, the Pope downplayed the use of Greek in the western churches favoring Latin, and the Patriarch downplayed the use of Latin, favoring the local languages, Greek, Russian etc.
First my qualifications- I'm an Orthodox convert from the Anglican church.
These were the issues- first the role of the Pope of Rome. Everyone greed he was the lead Bishop however the role was the issue. In the Orthodox church all Bishops are equal and an archbishop, metropolitan or Patriarch simply chair the meetings of the councils. In the west because Rome was loosing it's importance due to the fall of the Western Roman Empire the Pope wanted to strengthen his roll.
The west did start adding the Philippe then Finlay everything came to a head in a dispute over Churches in Sicily which both the Pope and Patriarch of Constantiople were claiming. The Pope issued a bull of excommunication and the Patriarch did the same.
The major event that is often cited as the separation of the East and West is the Great Schism of 1054. Actually at the time it was seen as simply another temporary schism between the two regions. But this one never resolved as the two Churches drifted farther apart. Also, though the date seems to be an easy reference, it must be seen as wider political and theological context which lead to the division.
One point not mentioned in some of your answers was the calender , weather to follow the Jewish Calender (Nisan) The Roman Catholic Church lead by the Pope(Chair of Peter maintained that the Calender was significant because the Day of Resurrection, and what time of year it fell upon...If you notice in the orthodox it varies greatly some times...