The Catholics reject several of the specific canons of the early ecumenical councils, but the orthodox accept them as inspired.
Catholics and Orthodox disagree on the dates of Christmas and Easter. While the Orthodox church claims council at Nice was inspired, yet is rejects the canons of Nicea on the date of Easter which the Catholics accept.
The Catholics teach purgatory, yet the Orthodox reject it.
Universal papal jurisdiction was a rather large dogfight in 588-606 AD.
Although the Orthodox reject Papal infallibility, the decisions of the orthodox synods are considered infallible.
The Immaculate Conception is utterly rejected by the Orthodox.
The orthodox baptized by full immersion (thrice), the Catholics sprinkle.
In the Orthodox Church married men can become priests. In the Catholic church men are forbidden to marry. (except for one small part of the world)
The Roman Catholic church introduced instrumental music no earlier than the 7th century and the Orthodox church has never used instrumental music, but like the apostles, sang without instrument.
In Catholic communion, the cup is withheld from the members, while the Orthodox float the "crouton looking" bread cubes in the wine. Catholics believe the bread and wine (transubstantiation) become the literal body of Christ when the priest says, "this is my body". The Orthodox disagrees and says the change takes place at prayer. Catholics use unleavened bread, while Orthodox use leavened bread. Orthodox must keep a ridged schedule of fasts in order to have communion every week, but the most common practice is a minimum of four times a year during the four Orthodox Lents "Christmas, Easter, Peter and Paul, The virgin Mary. Catholics on the other hand, must not eat the hour before, to have communion every day. In the end, Orthodox offer communion weekly and Catholics daily. In practice most Orthodox laity have communion four times year and Catholics weekly. So which of these two traditions is the one the apostles used? All this proves that they have no valid "apostolic tradition", otherwise they would all agree! They differ on the frequency of communion, the fasting requirements and the actual method of partaking.
Transubstantiation is a false doctrine that says the bread and grape juice of the Lord's supper actually molecularly change to become the flesh and blood of Jesus. Of course this old doctrine was formulated before the advent of molecular microscopes which see no change. For Catholics the "Transubstantiation" occurs when the priest says the words, "this is my body". For Orthodox the change occurs when the priest offers the prayer of thanks.
The "Filioque" scandal: Following the Nicene creed, the Orthodox Church believed the Holy Spirit proceeded from the Father alone. Then in 1054 AD the Roman church added to the wording of the Nicene creed "And the Son" or the "Filioque." The Roman church believed the Holy Spirit proceeded from BOTH the Father and the Son.
Orthodox keeps the original Nicene Creed, accepted by the Universal Church, East and West, during the first millennium without the addition of "And the Son" or the "Filioque." It accepts, on faith, Christ's words in the Gospel, that the Father is the Unoriginate Source of the Life of the Trinity, with the Only-Begotten Son and the Holy Spirit Proceeding from the Father Alone. We cannot know how the Begetting of the Son and the Proceeding of the Spirit from the same Father is different, only that it is and this distinguishes the two Persons