There are things about Orthodoxy that a Protestant may find wrong-minded and in some cases even heretical. And since for the Protestant reader at first introduction Orthodoxy looks like Catholic, let me say first that there is about as much difference and disagreement between Orthodoxy and Catholicism as there is between Protestantism and Catholicism. The Orthodox have never had a Pope, for one thing. Orthodoxy and Catholicism separated in the 11th century, thereabouts. Then in western Europe Protestantism split off from Catholicism starting, say, in the 1400s.
The next thing I should say is that Orthodoxy is centered on the worship of the triune God – God the Father; God the Son, Jesus Christ; and God the Holy Spirit. You can learn a lot about Orthodoxy theology through its worship services.
Moving on to he potential sticking-points, here are some Orthodox practices that Protestants often find wrong-headed:
Apostolic Succession: New bishops are raised to position by existing bishops, and this goes back to the apostles. Not in the apostolic succession? Not the Church … unless there is an exception. For this reason, Orthodox are not to take communion with non-Orthodox … unless there is an exception.
Tradition: Orthodoxy is not sola-scriptura. It teaches that, while Church tradition will not contradict scripture Church tradition, prayer, and a godly life are needed to properly frame and understand what the scriptures mean. It was, after all, Church councils (made up of prayerful, godly men) that determined what should and should not be in the canon of scripture that we call the bible today. The Orthodox include the apocryphal books that the Catholics use, plus two more.
Prayer to the Saints: I say it that way for the shock value. The Protestant view is that only Jesus should be prayed to and so “prayer” to the saints is heresy. But the Orthodox take “the cloud of witnesses” to literally exist and so we regard the saints that have passed on as alive. Based on that we ask these our brothers and sisters in Christ to pray for us. It looks like prayer because they are “dead”.
Veneration of Icons: This is an interesting one. It is regarded by Protestants as the worship of idols. I like to get at it this way: Would you, if you had been a soldier at war in a foreign land and thought that you would not live to return home, possibly kiss the earth when you returned to American soil or to your own home? Would you if under persecution have been unable to see a bible for some long time, kiss a bible if by some miracle God provided you one? Icons represent to the Orthodox that great and heavenly land and kingdom we are presently exiled from. They all represent born again people and/or angels and when we bow before them and kiss them we are showing our love and respect. It’s also a good time to ask them for a blessing (see “Prayer to the Saints” above).
High Church (Pomp and Circumstance): The services are designed to use all the senses to teach and to induct the participant into the presence of God … chanting, singing, incense, various implements, vestments, icons …
Deification: Here’s a doozy. Does the Orthodox become a god?? The Orthodox call deification what the Protestants call sanctification. It is the process of growing up into an increasing experiential union with and expression of God, the Holy Spirit.
I don’t know whether I have missed anything…