In Luke 9, Jesus sends the apostles out to do work such as healing the sick and casting out demons. In examining Jesus' instructions here and elsewhere, the SAB asks, Did Jesus tell his apostles to go barefoot and without a staff? I dealt with this before, and it was a subtle one. My understanding of what seems to be a contradiction here is that Jesus told them not to bring an extra staff, and wanted them to wear sandals rather than heavy shoes.
Apparently some people thought that Jesus was John the Baptist back from the dead, and the SAB wonders if Herod was among the people believing this. I think there's room for that interpretation in the Luke passage; although Herod doesn't actually say it, he does seem to be worried by the rumors.
Verse 27 has the cryptic message, "But I tell you of a truth, there be some standing here, which shall not taste of death, till they see the kingdom of God." This is an odd statement, and many people have interpreted it to mean that the second coming of Christ would be within the lifetimes of some of his apostles, but I don't think that's what it does mean. In all of the Gospels recording this claim, it is immediately followed by the event known as the Transfiguration, and many Christians believe that it was this event to which Jesus was referring, that is, seeing Christ transfigured was equivalent to seeing the "kingdom of God". (Luke says the Transfiguration was eight days after the speech, which disagrees with the other Gospels; I don't believe I have anything useful to shed light on the discrepancy.)
Shortly after this, Jesus cures an epileptic boy by casting a demon out of him. The SAB says that the Bible is implying that epilepsy is caused by demons, but all I think you can say is that the Bible is claiming it was in this particular case. For some reason, Jesus has some harsh words for his disciples for not being able to handle the demon on their own, I have no idea why.
A following passage that discusses casting out demons leads the SAB to ask two similar questions: Who can cast out devils in the name of Jesus? and Is casting out devils a sign of a true Christian? I don't think there's a real contradiction here, both really depend on a very particular interpretation of Mark 16:17, which in my opinion means that if you're a Christian, you should have the power to cast out demons, but that doesn't mean that if you can cast out demons you must be a Christian. Furthermore, I don't think that the people being discussed in this passage are necessarily not Christians, they're just not part of the main group of Jesus and his Apostles.
Did the Samaritans receive Jesus? This is a simple one to answer. Some of them did, some of them didn't. The story happening here is a different one than the one in John 4, and in this particular case, Jesus was not received. While I don't agree with the absurdity of Jesus' disciples asking to call down fire from heaven, I readily admit that it opens up some questions. Were they right in being angry? Would they have really been able to call down fire? What did Jesus' response to their request really mean? I don't know that anyone has answers to those questions. I sure don't.
Final note on this chapter: the man who asks Jesus, "Lord, suffer me first to go and bury my father." doesn't have a dead father, he's saying "I'd like to follow you, but can I wait until my parents are dead?" Perhaps one can still consider it cruel for Jesus to deny the request, but it's not what the SAB makes it sound like.