The first issue raised in Matthew 8 is the question of whether the centurion who asked Jesus to heal his servant came directly to Jesus, or sent messengers. While of course it could be possible that these are two different centurions, I think it's more likely that Matthew left some details out of the story. Note that in both stories, the centurion tells Jesus not to come to his house, so not coming in person makes some sense. The SAB points out that this would have been a good opportunity for Jesus to make a statement condemning slavery, but Jesus says nothing about this guy owning a slave. While I touched on this subject before, that was essentially discussing Israelite slavery, and this guy is a gentile, so I have little reason to assume that this is the same sort of arrangement. If I were to address the issue of slavery in the New Testament, I'd have to do some research, I think, but no, Jesus never comes out expressly against slavery as far as I'm aware.
The SAB makes a side-note on this story suggesting that perhaps the centurion and his servant were a gay couple. I find this difficult to fathom. Yes, I think in that day homosexuality may have been considered acceptable in Roman society, but what sort of couple would they have been if one was the owner of another? No, I think homosexuality is another issue that Jesus never directly addresses, even by silent assent.
In verse 10, we are told that Jesus was "astonished" and the SAB takes the opportunity to ask "Did Jesus know everything?" First of all, I think that Jesus expressing an emotion that is often linked with being surprised does not immediately mean that Jesus didn't know something, but I'll set that aside, because it's my view that Jesus, in the time that he walked the earth in human form, was not omniscient. The two quoted verses from the book of John aren't Jesus claiming to know everything, but his followers making that claim. The real nail in the coffin of Jesus having omniscience is Mark 13:32, in which Jesus admits there is at least one thing that he does not know. Now how much Jesus does know is worth questioning, and indeed, he does seem to know quite a bit, but he does not know everything.
Verse 12 is another odd one, and for more than just the reason the SAB notes. Yes, I'll agree with the interpretation that "the children of the kingdom" most likely refers to Jews, but that doesn't mean that all Jews will fail to be saved, I think that the point here is that despite the fact that the nation of Israel is the "chosen people", there will be many non-Jews in heaven and many Jews in hell. (I'm not really convinced that Jesus is even saying the the centurion is saved, only that he has an impressive level of faith.) The thing that I find interesting that's not noted is yet another use of the phrase "the children of..." that clouds the picture of what standing various people have before God, as discussed in a few of the recent chapters.
In verses 14-15, there is mention of Peter's mother-in-law being healed. The SAB asks, no doubt semi-sarcastically, whether this implies that the first Pope was married. Yes, Peter did appear to be married, and I don't know the full details, but it's my understanding that requiring clergy of the Catholic church to be celibate is a development more recent than the first century. I don't know if this goes for the Pope also, or whether the Catholic church thus has some explanation of this passage because of that issue; you'd probably have to ask a Catholic, not an ex-Jewish baptist like me. (The SAB marks this healing and the following casting out of devils as absurd; I'm not generally going to address miracles marked as absurdity, I think, but let them stand as miracles.)
Verses 21-22 have a man who wants to follow Jesus, but says "suffer me first to go and bury my father." I think the SAB is misunderstanding what the guy is asking here; it's always been my understanding that this was his way of saying, "I don't think my father would approve of me following you, so can I wait until he's passed away?" Jesus' response is not to literally suggest that dead people should bury each other, but that if his father can't handle Jesus, then he should be left behind. (This could still perhaps take all the tags the SAB gives it, but the meaning is not quite what it's being taken as.)
The story in verses 23-27 is another miracle, and I think the real point of the miracle, if anything, is what it says in the last verse: that even the weather obeys Jesus' commands.
The last story in this chapter is an odd one about Jesus casting out some demons (or perhaps one very strange, powerful one). For reasons unknown, when Mark and Luke tell this story, they say there's only one demon-possessed man, while Matthew puts it at two. I have no idea why the difference in number, and it seems to be a big difference; I mean, who has a hard time counting to two? (Matthew does use different names in his telling of the story, so it could possibly be a different event, but there's enough detail in common to make this improbable.) Anyway, this is an interesting story for numerous reasons. The demons immediately know who Jesus is, and they refer to some time in the future that Jesus is going to torment them. Weird stuff. Note that in other versions of the story, Jesus finds out that the devil(s) is named "Legion", and in all the stories, they are sent into a herd of pigs. Some have suggested that this story is symbolic of the Roman occupation, which is possible, but I'm not real keen on that interpretation. It is odd to note that someone in a Jewish city would be keeping a herd of pigs, seeing as they're unclean animals. I find it odd that people who dislike this story object to the drowning of the pigs; I guess while I'm thinking it's good that the demons were driven out at all, these people are wondering if it could have been done more cleanly. Certainly the people of the nearby town seem to think so, as they ask Jesus to leave.