Here are the things I think are important when considering this question:
(And as always on this discussion forum, I speak for myself, not BioLogos as an organization. Evidently this is hard for some people to grasp.)
First, Jesus grew in wisdom and stature. (Luke 2:52) I take this to mean his mind developed along with his body in the normal way, and there is no reason to think that his brain was somehow physically different than any other human brain. Human brains have physical limitations. Learning requires experience and trial and error. Why would we assume that when Jesus was learning to be a carpenter, he never measured a board wrong, or hit his thumb with a hammer? Making mistakes is part of learning. Jesus had to learn to read like any other kid. Why would we assume that he never confused two letters and read the wrong word? When he was memorizing Scripture in the synagogue, why would we assume he got it right the first time he tried, with no mental effort, no self-correction, no leaving out a phrase? When he was hanging out in the neighborhood doing whatever the Nazareth equivalent of shooting baskets was, why would we assume he made every single one? Being human and learning to do anything involves making mistakes and failing to execute a given task flawlessly.
Well, someone might say, how do we know Jesus was limited by his physical body and brain like other humans? He walked on water, he disappeared from the crowd that wanted to kill him, he knew every thing the Samaritan woman had ever done. Good points. But he also got tired (he was sleeping in the boat during the storm), hungry (he was weakened by his fasting in the wilderness), anxious (the whole sweating blood thing in Gesthemane), and hurt (the flogging/crucifixion), so we know his body/mind responded in normal human ways to stimuli. He wasn't just God walking around in the shape of a human. That is actually a heresy (docetism) rejected by the church at Nicaea in 325. I think it is fine to assume Jesus walked into a room and forgot what he was there to get, couldn't remember someone's name after being introduced only once, called his brother Simon, James once or twice, and any number of normal human "mistakes" caused by the limitations of our physical brains.
Second, Jesus spent an awful lot of time in prayer according to the Gospels. Why? Personally, I think it was because while he was incarnate he had the same access to the mind of God that the rest of us humans have, through the Holy Spirit. Unlike us, there was no sin or spiritual brokenness to get in the way of his prayers, but I don't think there is any indication that Jesus was omniscient. He had to pray to know the Father's will. There were things he claimed he did not know. (Mark 13:32, Matt 24:36) Why would he pray that "the cup be taken from him" in the Garden of Gesthemane if he was omniscient? So, how did Jesus supernaturally know things about people? I believe the Holy Spirit reveals truth and special discernment to people's minds in order for them do ministry. I have been around Christians who have had information about people and situations revealed to them spiritually in prayer, and obviously Jesus was sensitive in a unique way to the Holy Spirit's leading. I think all the knowledge that was necessary for his ministry and to perform the signs that singled him out as the Messiah were revealed to his human mind by the Holy Spirit. Would this revealed knowledge have included things like Newton's second law of motion or the fact that horses belong to the order of odd-toed ungulates? I doubt it. What bearing would that have on his kingdom work or Messianic calling?
So, all that brings us to the question, if someone had asked Jesus how old the universe is, would he have said "4.5 billion years"? Probably not. That would not be a fact taught in school for Jewish boys, and why would the Holy Spirit have revealed that knowledge to him? So was he "wrong" in his conception of the world on this point? Does it matter at all?
I think we can go too far in making Jesus out to be a product of his culture too. It is clear that he was not constrained by the prevailing ideas of his time and place about many things - the value of women, children, and cultural outsiders, for example. So we need to be careful when we say, "Well no one at the time thought X, so obviously Jesus didn't either." He did blow people's minds with his unique perspective on many things. I would say, that was because he was God incarnate.
When Jesus was telling people to turn the other cheek and walk the extra mile, and give their shirt as well as their cloak, these were direct references to the rights Roman soldiers had to make demands of Jewish people. Jesus' instructions were emphasizing that his kingdom was not of this world and he wasn't there to help people throw off Roman rule and rebel. He was teaching people to thwart the unjust systems of the world with love and service, which is actually a brilliant form of resistance. "Turn the other cheek" is an example of the importance of understanding the context of Scripture and the intent of a given command. Jesus wasn't talking to a battered woman or a sexually abused child.