I think Matthew 12 is the first time we see Jesus and the Pharisees go head to head on the matter of the Sabbath, something that happened a lot in the Gospels. It's always been my understanding that the substance of these arguments has a lot to do with the complicated oral traditions that had risen over the centuries (and are still observed by most Jews today) that explained what the Mosaic Law meant in fine detail. In this case, picking grain is considered by the oral law to be the equivalent of harvesting, and thus work, which was forbidden. No, this matter of priests who "profane the Sabbath" is not a specific verse, but I think it's a general principle: that while normal people don't work on the Sabbath, priests at the temple actually have quite a bit of work to do.
Is it necessary to keep the Sabbath? I addressed that back in Exodus 16, but there's probably a bit more that could be said. I think the Sabbath is a good thing, and I think it's something that God intended for everyone. I think the problem that Jesus is addressing in these exchanges is one that struck me as a child being raised Jewish: sometimes religious people can take what are good ideas and make them so complicated and confusing that they stop being so good and become a stumbling block. In the Jewish community, the Sabbath rarely felt like rest to me as a child, and when things get that way, they may be counter-productive. (I addressed the question about David when I covered 1Samuel 21 and the question about animal sacrifices in Genesis 4.)
Following this in the narrative are a series of miracles, to which the Pharisees make the claim that Jesus is doing the things he does because he has demonic power. The SAB points out that strategically this might make sense, and clearly it makes some sense or the Pharisees wouldn't have said it, but Jesus addresses the idea in verse 25, whether you buy his logic or not.
Who is for or against Jesus? the SAB asks. This is an interesting question, as it shows me that there is at least some recognition of poetic language, since on the face of it, there's no contradiction; the contradiction is in understanding the deeper meaning of the phrases on the linked page. I think that however you take those phrases, the conclusion is the same: Jesus doesn't believe in neutral ground when it comes to his allegiances.
Is there an unforgivable sin? This would obviously be a vital question theologically; unfortunately the answer is not obvious. I'm not sure what the consensus is, I'll give my view. Jesus speaks here about "blasphemy against the Holy Ghost", and seems to be saying it's an unforgivable sin, but what exactly is "blasphemy against the Holy Ghost"? Since Jesus brings it up at this moment, it seems likely that it's related to the current situation, and has something to do with denying the godliness of the work that Jesus is doing. Perhaps denying the godliness of the work of the Holy Ghost is key? I like to lean on an explanation that happens to explain away the contradiction, though. The (supposedly) contradicting verse is Acts 13:39, "And by him all that believe are justified from all things." What is it that the Holy Ghost does in a believer? He convicts of of our sins and turns us to Jesus; thus the unforgivable sin is refusing to allow the Holy Ghost to affect that change in your life, and thus refusing belief in Jesus. If refusing to believe in Jesus through the power of the Holy Ghost is the unforgivable sin, then there is no contradiction.
The SAB points out that Jesus sometimes used some harsh words for his adversaries, and yeah, that's true. I don't follow the next note that says that men being made accountable for their words is supposedly unjust. I'm pretty sure even earthly justice systems make people accountable for things that they say.
How are people judged by God? This is a complicated question. One reason that it's complicated is that I think there is more than one level of judgment. In the end, you go to Heaven based on faith, but I don't think that everyone gets the same rewards in Heaven. I think the other issue is that when a verse like John 5:29 says, "they that have done good," it may not be clear what "good" means. Perhaps these people have done "good" by believing in "good" things, and thus "they that have done good," are those who believe the right things. I'll admit it's a bit sketchy. The question "Is anyone justified?" is similar. I don't think that any person is justified in himself, but their words will belie what they believe, and it is their belief that will allow them to be justified by the grace of God.
Did Jesus perform many signs and wonders? Well, the obvious answer is "Yes." So what's with the "No" column verses? I think the point that Jesus is making in those declarations is not that he won't perform miracles at all, but that he won't do them for the mere sake of showmanship. Every miracle that Jesus performed was done with a practical purpose in mind, not just to show off.
Was Jonah swallowed by a fish or a whale? I've seen this one come up in a group of Christians, actually. I don't know why people argue over matters like this, though; it's a linguistic matter. In ancient Israelite culture, the way animals were classified was much simpler than they are today, and had little to do with modern biology. It's like this: if it lives in the water, it's a fish. So by the simpler Biblical classification system, even if it was a whale, it was still a fish.
I answered the question about Jesus vs. Solomon in the previous chapter, and I'm not sure what to say concerning unclean spirits, so I'm moving on.
I don't think that Jesus is trying to say in the little vignette at the end of this chapter that one should not respect one's family, rather I think Jesus is trying to say that for him, his family was bigger than just his blood relatives.