Is the Bible inerrant?
The word "inerrant" is not in the Bible. I prefer to stick to the wording of the Bible, particularly when it comes to doctrines. People who like to generalize tend to overgeneralize.
2 Timothy 3:
See
Is the Bible the word of God?.
I would never say that flawed Peter or Paul--flawed at their own admission--could write a letter with no spelling errors. Can we do that all the time even with a spell-checker? ;)
What I will say is that Jesus chose 12 young men to spend time with every day for at least 3.5 years. I would assume this is because Jesus realized they might get his teaching wrong, and they needed daily help in pinning his teachings down. He was always available to explain things when asked.
So the apostles were able to come to a consensus about what Jesus' message was, and their agreement happened in the very presence of Jesus. That's why Paul visited the apostles and James, to determine that his own teaching and revelation was in perfect alignment with what Jesus had taught his apostles.
I *love* how you're putting this--Scripture is "God-breathed," keeping to just what the Scriptures say, and not adding all kinds of insinuations that simply aren't there. I can't believe any of the Scripture writers were perfect. But I believe God chose responsible men to accurately share things with the world and history. The Bible is clearly an inspired book. Even more, it is completely reliable in its messages.