4. What is the key to the correct understanding of the Bible?
The answer indicates that the core to meaning the Bible is Jesus. In other words, whatever is read must be understood in light of the death and resurrection of Jesus. In some things this may be hard to notice. Parts of the Old Testament gain new meaning when you factor Jesus into the equation. Often I am inclined to read the books of the Bible as separate works with different genres. But they are unified through the message of Jesus.
5. How is human reason to be used in understanding Holy Scriptures?
The thing that interests me is how the answer indicates that it's OK to use reason when trying to understand the Bible (including philosophy), but it has to be subject to the Holy Spirit. This is another strike against the claim of fideism I've put on Lutheranism in general.
36. Does God require us to observe the Sabbath and other holy days of the Old Testament?
This is one of the more radical things I've read thus far. Radical in the sense that the answer indicates we as Christians are not required to pick a day to observe as a Sabbath. Rather, Jesus Christ is our Sabbath, our rest (Matt. 11:28, Matt 12:8, Col. 2:16-17, Heb. 4:9-10). Through Jesus Christ we have a perpetual, constant Sabbath rest even if we're not physically relaxing.
37. Does God require the church to worship together on any specific days?
The answer here is that while God does command us to worship together, there is no day we're required to meet up on. Most Christians have church on Sundays. Seventh Day Adventists prefer Saturdays. There is no set date for it. Indeed I have seen instances of churches holding services on Sunday, but also Wednesdays and Saturdays. Sunday is the normal day of worship mainly because that's the day Jesus was resurrected on.
I was surprised at this answer. The catechism says "yes" - lawful governments are authorized to execute criminals and fight just wars, which include taking lives.
56. What does God forbid in the Sixth Commandment?
Divorce is unacceptable except in cases of marital unfaithfulness. This includes adultery, but also desertion. From the Bible verse used to support the desertion parts it seems to imply the deserting member is an unbeliever. Maybe it's also expanded to believers as well. I'm a little surprised abuse is never considered a reason for divorce. I personally would not bat an eye over that being a reason people get divorced, because it strikes me as completely out of God's will for someone to remain with an abusive partner.
71. What does God mean when He threatens to punish the children for the sin of the father to the third and fourth generation of those who hate Him?
It seems Martin Luther didn't realize that the above statement wasn't meant to literally mean punishment for sin would extend to one's children. He cites Ezekiel 18:20 saying that sons will not be punished for their fathers' sins. The statement the question addresses, if I recall correctly, is a reference to how the gods of the neighboring nations actually would place a generational punishment like this. By mentioning it, God speaks of how powerful he is. It is a sort of metaphor which speaks of God's sovereignty.
80. How many kinds of sin are there?
The catechism mentions two types of sin: original sin and actual sin. Actual sin is the stuff we do, and nobody seems to deny it's there. Original sin states we are wholly corrupted due to the first sin ever committed by Adam and Eve. I know this is something not everyone agrees with, although I haven't really focused much on it.