Luke 6 does open with a bit of odd wording, as the SAB notes, but it quickly develops into a story that's a common one for the Gospels: arguments between Jesus and the Pharisees over the technicalities of the Sabbath. It's good to note first of all that what Jesus and his disciples were doing was not considered stealing in that culture. When a person passed through a field of grain or an orchard, they were allowed to pick whatever they could eat as they walked. The Pharisees however still considered the picking of grain to be an act of harvesting, which would be work, and therefore unlawful on the Sabbath. Jesus brings up the story of David taking some bread from the Tabernacle in a time when he was desperate, the point being that when you're hungry and desperate, you shouldn't let tradition stop you from eating. (The idea that picking a few heads of grain to eat was harvesting was not part of the Mosaic law, but rather Jewish tradition.)
The SAB asks regarding this story, Was David alone when he asked for the holy bread at Nob? I think this is a misunderstanding of the passage in 1Samuel, as you can see in verse 21:4 that the priest says "...if the young men have kept themselves at least from women." If David is alone, then who are "the young men" being referred to? David was not alone, although he may have come into the presence of the priest alone.
The SAB marks Jesus' act of healing a man's hand with the "science" icon. I'm never sure if I really need to comment on such things. Jesus did a lot of supernatural things, which are of course going to go against science. What is there to say about it?
The SAB asks Who were the apostles? and shows that in each of the four Gospels, there's a list, and none of the lists are completely identical. The most likely explanation for the discrepancy is that many of the apostles had more than one name, and so Jesus may have given a secondary name to Judas the brother of James, and that name was apparently Lebbaeus Thaddeus.
Did Jesus preach his first sermon on a mountain or a plain? This appears to be the so-called "sermon on the mount", but Luke clearly states that this is happening on a plain. There are a couple possibilities. First, this may have been one of several similar sermons that Jesus gave in a few different places. Second, the way the sermon is described in Matthew's Gospel seems to set up the acoustics all wrong; if you stand on a mountain with people below you, it's going to be hard for them to hear, so it would make more sense that Jesus found a place with a mountainside near a plain to set up a sort of natural amphitheater. In that case, the answer would be "both".
In verses 24-26, the SAB has a series of questions that I'm going to answer as one. I don't think that this section of the sermon is suggesting that these people are going to Hell. What I do think is going on is that like the things before Jesus said one would be "blessed" for, Jesus is suggesting that there is going to be a reversal of the status quo. Why he's suggesting this, I'm not really sure, but I've heard it said time and again that the "sermon on the mount" isn't about salvation issues, but rather about earthly issues.
Verse 27 is marked as "Good Stuff", but is also marked as contradicting other passages. In the issue of How should enemies be treated? I think one needs to see that the verses in the second column are, for the most part, not commands about how to treat enemies, but rather individual instances of people having less than charitable reactions to enemies. The exception to this is the very last verse given, but I think that verse fits in better with the second question, How should nonbelievers be treated? In this case, and on that page, there are a few different issues being dealt with. In the first verse, this is a specific law given to Jews with respect to their fellow Jews. Yeah, it seems pretty harsh, but its purpose is to keep religious purity within the nation of Israel. In the second case, I think "shun them" is an overstatement of what's being admonished here. Most people that I know of interpret this verse to mean that it's best to not enter into business partnerships with unbelievers if possible.
Verses 29-30 have Jesus suggesting some rather extreme acts of kindness, taking "Love thy enemy" to its full extent. The SAB marks the passage as absurd, and really, it is. I think it's a difficult passage that the Christian has to decide whether it was meant to be taken literally or whether it may have been hyperbole, but Jesus appears to be sincere.
Is God merciful? It's hard to sugar-coat this one; the SAB comes up with a lot of verses that seem to show God being unmerciful, some of them even saying outright that God is not showing mercy. The fact is that while God called merciful several times, this is not an attribute of God that He displays all the time. It's a common theme of Christian sermons that we can see that God is merciful because every single one of us is a sinner, and yet God doesn't simply send us all to Hell right this moment. That's certainly a matter of perspective that I don't expect too many skeptics to buy into unless they really understand the issue of sin and how it effects our standing before God. It's probably not something I can really explain, but would be willing to try in the comments so as not to make this post twice as long as it already is.
To judge or not to judge? I think most unbelievers are familiar with the Bible verse, "Judge not," but miss that there is more to the phrase. Here in Luke, the full verse goes, "Judge not, and ye shall not be judged." In any case, the verses in the Bible that warn against judging are not saying that a person cannot judge, but rather are warnings that when you become a judge, you are going to warrant others, including God, to judge you in return. While this may not rule out judging completely, it should give one pause. As Jesus goes on to say here, you may be judging someone for a little speck of sin when you have an entire log in your own eye. That's not a good place to be.