The Catholic Church will need to do some serious soul searching in terms of what precisely it has taught on any subject that might differ from that taught prior to the split and where that teaching stands in the heierachy of theological truth.
No. Christ’s Catholic Church does not teach any doctrine or dogma that is in error.
The Catholic Church has always been the only Church established by Jesus the Christ, but from the beginning there have been dissenters and heretics.
There is the Latin Rite, and the Eastern Rite of the Catholic Church with the same dogma and doctrine; naturally, all of these are in union with the See of Peter and assent to Papal Supremacy.
With free-will and selfism, St Paul attests: “I know that after my departure…of your own selves shall arise men speaking perverse things to draw away disciples after them.” [Acts 20:30].
The Orthodox Churches have broken with the See of Peter since 1054, and are individualistic among themselves. Since "legitimacy" means "lawfulness by virtue of being authorized", it is hardly reasonable to assume that the Orthodox Church has the same legitimacy as the Catholic Church in the mind of Christ, who gave His authority to Peter and his successors to teach, sanctify and rule, and whose supreme authority has been shown in the NT, if Peter's authority is not recognised.
It is not only respect but obedience that is required. The third successor of St Peter, Clement, wrote to the Catholics of Corinth in A.D. 95: "If any man should be disobedient unto the words spoken by God through us, let them understand that they will entangle themselves in no slight transgression and danger... Render obedience to the things written by us through the Holy Spirit." (I Clem. ad Cor. 59,1).