[I know that the orthodox church was the first to split off, right? ]
WRONG! We never split from the authority of Rome because we were never 'under the authority of Rome'. Administratively, what is now known as the Roman Catholic Church did not function as it does now in the first thousand years of Chritianity. The Patriarch of Rome was one of five patriarchates. Because he resided in Rome, which was the capitol of the then known Roman Empire, he had a 'primacy OF HONOR'. He was looked upon as the 'first AMONGST EQUALS' . He never had the so called supremacy over the entire christian church he claims now. Recommend the following website for the Orthodox Catholic view regarding so called 'Papal Primacy' which is really 'papal Supremacy' -http://aggreen.net/peter/st_peter.html
[What keeps them from being catholic?]
Absolutely nothing! We Orthodox, contrary to what the Roman Catholic Church teaches, never left that 'One Holy Catholic and Apostolic Church' mentioned in the Nicean Creed. We are still it in it's original unadulterated form. We have neither added to the faith of the first seven ecumenical councils (like the RCC), nor have we subtracted or changed the faith of that church of the first seven ecumenical councils as both the RCC and the Protestants have. We, more than any other church, best fit the description of St Vincent of Lerins on the definition of what it means to be a Catholic -
A General Rule for distinguishing the Truth of the Catholic Faith from the Falsehood of Heretical Pravity
That we hold that faith which has been believed everywhere, always, by all. For that is truly and in the strictest sense "Catholic," which, as the name itself and the reason of the thing declare, comprehends all universally. This rule we shall observe if we follow universality, antiquity, consent. We shall follow universality if we confess that one faith to be true, which the whole Church throughout the world confesses; antiquity, if we in no wise depart from those interpretations which it is manifest were notoriously held by our holy ancestors and fathers; consent, in like manner, if in antiquity itself we adhere to the consentient definitions and determinations of all, or at the least of almost all priests and doctors.
[Do you disagree on any theological issues like the big ones such as Mary, eucharist, confession, icons etc?]
We do not believe in the 'Immaculate Conception' of the Theotokos. Eucharist we receive in 'both' species rather than one. Though we both believe that the bread and wine becomes the body & blood of Christ, we disagree on when and exactly how that happens. We Orthodox see it more as a mystery which needs no exact formula to happen. It is one of God's mysteries. Confession is similiar except our priests don't ask questions like when, where, why, and how many times? God is well aware about what we are confessing. We both have Icons. Orthodox Catholics more so than Roman Catholics.
Hope this helps.