The Orthodox Church
With the Orthodox Church, you have the best resemblance to early church teaching. Yet, this does not mean the Orthodox Church is free of all error. I would say they are the best preserved in the original Apostles teaching, though some Protestant Churches have made good strides to reach this. The problem is in the Protestant church, you have to convince people to agree with you. Within the Orthodox Church, they have a balance of powers and tradition that allows for perfect preservation of their dogma throughout time.
Their structure is based on a similar structure found within the United States Government, namely a "Balance of Powers". They have a certain amount of Bishops who have equal power. And if one gets out of line, the others correct him or relieve him of his office. This way, doctrine is preserved. They also have a mass structure, which is very solid and controlled and they do not try to get into explaining everything and "setting in stone" every jot and tittle of thought within scripture. This helps them to avoid division and strife over trifling issues.
This allows for a very strong core design. Yet, I believe the error comes in that they lack in other areas. They do not seem very "up with the times" and have difficulties reaching the community around them.
I believe the Protestants probably have the best design for reaching out to people and seem the most "up with the times". And, honestly, the Catholic seem to have the best ability to work with secular governments to accomplish their agendas. If maybe all three churches could put aside their differences and work together, they would be able to accomplish a great amount in this world.
If the Pope would relinquish his total control over the Western church and agreed to work with the Orthodox and other Bishops within the Catholic church as equals, and returned to a more basic core doctrine and forsook the need to explain every doctrine to perfection, they could come to some agreement and work together. Further, if the Protestant church could rediscover its roots and focused more on the original languages of the Bible and the earliest church teaching, they could come to core agreement with the Orthodox Church and would be able to unite as well.
Some of the errors I have seen within the Orthdox Church are more a result of them attempting to be too careful with doctrine. Sounds odd, but one example is that no Bishop is married within the Orthodox Church, though you do find the occassional Priest who is married within the church.
The reason you do not find any Bishops married and only a few Priests married is because of their approach to theology. With the Apostle Paul's commands to Deacons and Bishops we find the scripture to say that a Bishop is "to be husband to one wife". They read this as a prohibition against polygamy, rather than a commandment for the Bishop to be married.
As a result of their belief that it is to stear Bishops away from polygamy, they go a step further and only allow non-married men to become Bishops. So, you can see an over cautiousness with their approach to the Bible passage.
You also see rigidness with how they view Communion and also Apostolic Succession. They take a very traditional rigid approach, only allowing those they know who are Orthodox to take Communion (not a bad idea, but not exactly perfect either). Also, with Apostolic Succession, we see their belief that only a Bishop of the Original Church can lead a church, so they claim that the Protestant church does not have such a Bishop (as there were no Protesting Bishops which left the Catholic Church to start the Protestant Church). Yet, this is faulty logic, if one looks at the earliest church fathers, as I have done here.
There are a few other things I think are odd and seem borderline unscriptural, but often it is a result of them being too careful with God's Word or allowing tradition to have too much free reign. Yet, one should not be so careful, as to violate other principles found in scripture.