They are not inerrant though. That's the topic.
You are mixing two different concepts.
The originals are inspired, just like our very slightly errant copies today.
The assumption that the originals must be inerrant is only essential if you hold to a dictation theory of inspiration, where the humans who wrote the Bible are only scribes who jotted down the exactly what God said. However the dictation theory doesn't seem to hold true for what we actually have in the scripture. For instance, Luke freely informs the reader, Theophilus ("lover of God"), that he has compiled the Gospel of Luke from many different sources (see Luke 1:1-4) in order to create an orderly account.
God has apparently allowed a lot of human latitude in the writing of the scriptures, where for instance, Paul gives his opinion about things but is careful to note that it is his opinion, not a command of the Lord. There are also variations in some of the gospel accounts according to the purposes and emphases of the Gospel authors. None of this should be troubling to us, but unfortunately an attitude of suspicion and unbelief through Western "modernistic" thinking has trained our minds to reject anything that is not "certain." Therefore, we tend to have difficulty accepting the idea that witnesses may see and comprehend different aspects of the same reality, yet be reliable witnesses without 100% accuracy. We can trust their testimony, especially since we have available to us the abiding presence of the Spirit and a living and intimate relationship with God.
We are not like deists who have only a holy book and each other... we have a living and interactive connection with God.
All that being said, I don't believe the Bible is full of errors. I think it is shockingly free of errors, especially for a book of its age, history, and the temptation for people to alter the text. I believe the scripture we have today is essentially inerrant for doctrine and praxis, although I reject the concept of inerrancy as a misplaced emphasis that does more harm than good. Because of the constant sniping and fighting over inerrancy, we spend too much time talking ABOUT the Bible instead of knowing scripture and putting into practice.