So here I am again, and starting over with the New Testament, in Matthew 1. As the SAB points out about this chapter, Paul writes in a couple places that genealogies are a waste of time, and yet as with so many other places in the Bible, we're here presented with not just a genealogy, but one that will lead to (as Titus 3:9 in particular warns against) "foolish questions, ... and contentions, and strivings about the law;" oh well. I'll dismiss the genealogy issue with a simple fact: I don't know what Paul had against them, so I'm going to gloss over that issue until I may happen to hit one of those passages in a future entry. I'm going to have plenty of other things to deal with here.
The first specific detail the SAB latches onto in this list is the mention of Tamar in verse three. Of course, that story is a rather racy one, so I can see why the SAB marks it with the sex symbol, but I'm not sure what the absurdity symbol is about. If it has something to do with the related cross reference to Deut. 23:2, it's something interesting I find worth noting: David was ten generations removed from Tamar, so while there are some hints in Genesis that Judah was intended to be the royal line of Israel, in the end, David was the first in that line to take the throne; perhaps it was because of the ten generations thing in the Deuteronomy passage?
The SAB goes on to comment on the inconsistencies between this genealogy and the one in Luke's Gospel, which is as par for the course in Biblical criticism as noting the apparent disparities between Genesis 1 & 2. In this case, there are a number of issues that I think are valid to bring up, and are not simple misunderstandings, although there are some good responses that some people have come up with. The usual response to the discrepancies on the whole is that one of these two genealogies is that of Mary, while the other is that of Joseph. This explains away some of the discrepancy, but admittedly may bring up other issues.
I've heard it said that this genealogy is that of Mary, since it's the one that mentions Mary, but that's a problem with the bigger issue of why Mary's genealogy is needed in the first place. If we skip down to the note on verse 12, the SAB asks "Did Jeconiah have any children?" which is actually an important question. As referenced on the linked page, Jeremiah 22 says that Jeconiah should be considered to be childless, but this is a bit of poetic speech, the latter part of the quoted passage explaining the real meaning: no blood descendant of Jeconiah was to ever be allowed to be king. Thus, while the royal line goes through Jeconiah, it was cursed by God in Jeremiah's time, requiring any future king of Israel to be a blood descendant of David, but only a legal descendant of Jeconiah. Since Joseph (the husband of Mary) was a descendant of Jeconiah, but Jesus was only adopted by Joseph, that gives Jesus the blood and legal requirements to sit on the throne. This is a complicated issue that I'm not doing justice here, but I don't want (nor do I likely have the wherewithal) to write a huge essay here on this single topic. Suffice to say that if this is the reason for the two genealogies, then this one needs to be Joseph's.
This also answers (albeit pretty weakly, I'll admit) the question on verse 16 regarding the identity of Jesus' paternal grandfather: it was Jacob son of Matthan, while Heli son of Matthat (confusingly similar name there) had to be his maternal grandfather. As for the rest of the issues, and particularly Matthew's odd fetish for the number 14, they have to do with, well honestly, Matthew was fudging the numbers, and very poorly. For reasons he doesn't explain, Matthew really likes this pattern of 14s. It has something to do with Hebrew numerology and some relationship between the Messiah and the number 14. I know the numerical value of the name "David" in Hebrew is 14, but beyond that, you'd have to look elsewhere. As I said, I'm trying to not stretch this out to ridiculously long, and I probably already have.