Luke 21 opens with Jesus giving commentary on some people giving money at the temple; in particular, he points out a widow who puts in a tiny amount of money as having "cast in more money than they all." The SAB deduces from this that Jesus is in favor of progressive taxation, but as usual I think extending spiritual truths that Jesus teaches into the realm of politics is iffy. Still, there is perhaps a principle at work here, and it may tie in with his claim from two chapters ago that it's hard for rich people to enter heaven. As a political liberal, I'd like to think Jesus favors progressive taxation, I just don't know how strong of a case you can really make from this one passage.
Most of the rest of this chapter is a rambling speech about the second coming: when to expect it, what to expect when it's coming, what sorts of things will happen before it comes, etc. A lot of this stuff sounds very violent and horrible, but I don't think that Jesus is saying he endorses the bad parts, only that they will be coming so be ready. (There's an interesting sub-point in this that the SAB points out, but only in passing; Jesus says some people are going to be put to death and yet "there shall not an hair of your head perish." Seems like a contradiction in terms there, doesn't it?)
Should we look for signs in the heavens? This may come across as a bit iffy to a skeptic, but I think that despite the passage mentioning signs, there is no admonition to look for them. It's not clear from context what these "signs" will be, and I actually expect that they will be false signs to confuse people further in the midst of all the chaos already going on. Speaking of which, Does the bible condemn astrology? I'm sure I've addressed it before but in general, the Bible does condemn astrology. Note that the Genesis passage says, "let them be for signs, and for seasons, and for days, and for years," which suggests to me that the passage is just pointing out the obvious that the positions of stars can work like a calendar. The Judges passage most likely is not talking about actual stars, but rather about angels, which in many prophetic passages are referred to as "stars". The passage here in Luke talks about signs, but once again, I think these may be false signs, which leaves only the Matthew verse to discuss. There are a couple of things to be said about the star of Bethlehem, one being that the people who followed it were not Jews. Secondly, and this is an interesting one that I recently read about in a Jehovah's Witness publication (although I'm not a JW, I read Watchtower Magazine and Awake! just because I find them fascinating), the star of Bethlehem somehow led them to the wrong king and put Jesus in mortal danger, so it has questionable value; the publication I was reading suggested it was a demonic sign, which I find a fascinating theory.
Will Jesus' second coming be visible to all? According to the note at the bottom of the page, I'm apparently not the only one who is interested in the teachings of the Jehovah's Witnesses, as the SAB has taken from them in some way this possible contradiction from a verse in John. I think the solution to this contradiction is a simple one, as there is nothing particular that indicates the verse in John will be forever.
In verse 32, Jesus says "Verily I say unto you, This generation shall not pass away, till all be fulfilled." The SAB suggests this is failed prophecy since it didn't all happen within the lifetime of his listeners, but that's making the assumption that "this generation" refers to his listeners. It may very well be that Jesus is saying the generation that sees the signs won't pass away until the end of the world. (Note that he talks about a fig tree; some scholars have suggested that the fig tree is symbolic of the nation Israel, and thus the generation that sees Israel restored is the one that will see the end. This idea has gotten a bit less popular as the time span from the reestablishing of Israel has increased.)
Will the earth last forever? I would say that this one is a rather metaphysical question. I think the theological consensus is that the earth will last for all of time, but eventually time itself shall cease to exist. In any case, when the "new earth" is created something about it is going to be fundamentally different on a cosmic level.