What would Jesus have learned as the son of a carpenter? What experiences would this have exposed him to?
Jesus was willing to do what his parents wanted, even when it didn't seem directly related to his purpose on earth. He was patient with the apparent mundane tasks of this life, realizing life experiences have value. While he never intended to be a carpenter, he would have had exposure just by the fact he was Joseph's son. Since the Bible says so little about Joseph, we are not sure how long he was alive and involved in Jesus life. So, it's hard to guess how much experience /exposure Jesus had to the trade of carpentery. But, he probably did have some experience just by living with Joseph and spending time with him. As belivers we can take comfort in knowing Jesus was doing the will of God and God was pleased even though every minute of his life wasn't directly related to ministry (especially in his growing up years). There are many things we do in our day to day life that do not relate to eternity directly, yet we can have peace and joy if we know we are in the will of the Father. God sees behind the scenes and is using tasks and jobs that seem of no eternal value to shape us and teach us.
The Mark 6:3 passage points to Jesus being a carpenter, I think the significance here is in Jesus being ordinary, from an ordinary family. Obviously Jesus was a teacher/Rabbi as his main purpose here on earth. The people who were having trouble with this were the people from his home town who remembered Jesus as "a carpenter" or ordinary. I think this applies to us, who have a past this is not impressive. While we may be a changed person now, it is often the people who remember us from years ago who have a hard time seeing us for who we are now.