There will always be an element of faith, but it doesn’t need to be blind faith.
As for the “errors”, there are several possibilities to account for this.
One reason is we have on the wrong glasses. We read it from a modern Greek perspective, not a Jewish perspective. It’s like you reading a Chinese book and saying it’s all wrong. You have to dig a little deeper to understand the culture, audience, and mentality of the Chinese and not judge based on western modern culture. Also, just because our glasses makes things look skewed doesn’t necessarily mean the Bible is skewed. Our modern assumptions of precision and accuracy did not exist in the minds of the authors. So, each account doesn’t need to match up in all the details. It is anachronistic to place on them a modern standard that they did not and could not have. Now, it’s entirely possible to read the Bible with our modern glasses on and to understand the core message. But to impose modern assumptions to demonstrate the Bible is wrong is anachronistic.
Another factor is our culture has a major impact in our interpretation of the Bible and makes things look skewed. An example of this is our modern debate on homosexuality. Actually, the Bible doesn’t say much about this. And Jesus didn’t say anything about it. Yet, given all the hoopla over it, you would think this is some major doctrine of the Bible. Another example is accepting Jesus as your savior by raising your hand, walking down the aisle, and accepting him in your heart. Who knows how many times this is done in the US each Sunday? Yet, this is not even in the Bible.