Does God approve of capital punishment? That's actually a very good question, and one that many of us wish had a simpler answer. The fact is, God's view of capital punishment in the Bible is a question that would require the study of far more verses than the two quoted here. You'd have to look at passages like the one in which a man is killed for gathering firewood on a Saturday, or where Jesus forgives a woman caught in adultery (but never denies that adultery is a capital crime!), and many others. The short simple answer is, yes, God does approve of capital punishment; the long answer would be an extensive study on what sorts of things God considers worthy of death, and why, and when and why God prefers mercy. I don't believe I'm qualified to give an adequate response of the long sort, but I'd be willing to discuss my views on it in the comments section if anyone really is curious.
Verses 8-17 talk about the covenant that God makes that He will never destroy the world again through a flood, and He offers the rainbow as a sign of that covenant. The main beef that the SAB seems to have with this concept is a scientific one, that being that rainbows are a natural phenomenon. Personally, I don't see why this should be a problem. Just because rainbows may have existed before this covenant was made doesn't mean that God can't use them as a symbolic gesture. Take the early Christians as an example. They were of the habit of using a simple drawing of a fish as a symbol of their faith. Fishes existed before Christianity did, but they decided to use the symbol for their own purposes.
However, my own personal theory that I admittedly have little scientific basis for goes back to the water canopy theory. It seems to me that if the entire earth was covered with a layer of water acting a shield of some sort, then sunlight may not have refracted in precisely the way it does today. Furthermore, regarding this theory, you might remember that I had briefly speculated that it may never have rained before the flood. If it never rained, then there would never have been a rainbow. All of this is in the area of wilder speculation, of course, and the more important aspect of this part of the story is the symbolic aspect. The rainbow, as we now know, is not an actual bow, but is instead a circle that we only see part of from our vantage point standing on the earth. God uses the rainbow as a symbol, knowing that when we look at it, it will look like a bow, but without an arrow on the string. The symbolism is that God has fired this weapon He has, and He intends to now set it down, never to pick it up again.
The rest of the chapter is pretty much all about the drunkenness of Noah and the curse of Canaan. This is obviously a very strange story, and a lot of it that nobody really fully understands. The SAB gives a link to an excellent article on The Straight Dope, a site that I have a great deal of admiration for in many of these matters. (Even when I disagree with their conclusions, I respect the scholarship that went into them and consider them about as unbiased as it gets on the Internet.) It does seem a little odd to me that they link to an article that gives some straightforward answers to many of the questions they raise right before the link.
First of all, being drunk doesn't necessarily mean that you're not righteous, and I think it's perhaps quite understandable that after seeing the entire world destroyed, Noah might feel the need for a good drink, whether out of shock or guilt or depression. Secondly, being naked is also not a sin, especially if it's in the privacy of your own home (or tent as the case may be).
"What did [Ham] do besides look at him?" the SAB asks. First of all, looking at him alone is not entirely inoffensive; I think Noah has a right to some privacy, and Ham's violating that. On top of personally violating his father's privacy, Ham goes and tells his brothers that this is going on, as if it's their business! Granted, on the face of it, there seems to be very little reason to go so far as to put a curse on someone, and even if Noah was justified, it's not too clear why he curses Canaan rather than Ham. The Straight Dope gives the only possibility that even begins to make sense to me, that being that since Ham shamed his father, Noah shamed Ham's son. I don't know, though really, although there are a number of interesting speculations given in the article there. Actually, something that occurs to me now is that since at this time Canaan is the only offspring of Ham mentioned, he may in fact be the only one at this time, and Noah may be using Canaan's name as a generic label for all the descendants of Ham. Not that it fully justifies the curse, but it might make more sense.
Does God approve of slavery? That's a tough question that has been struggled with for a long, long time. You may have heard this sort of response before, but I do think it's the correct one. Yes, God does approve, but it depends on the definition of slavery. In Exodus 21, it's made clear that among the Israelites that slavery is never to be a permanent thing, and furthermore, slavery is essentially a voluntary position. There are some exceptions that get complicated, but the idea is that if a person sank into poverty and could no longer afford food, one could sell oneself to another person (but you couldn't sell someone else), and then they were bound to serve that person for six years, or until their price could be paid back, whichever came first. Maybe it's not ideal, but it's not the same as we think of slavery from the early 1800s, not by a long shot. (For more observations on the nature of Biblical slavery, see this post.)
But the SAB asks the excellent question "Are we punished for the sins of others?" Yes and no. Sometimes, we end up having to take responsibility for the sins of our parents and grandparents just because it's the natural result of what they did. For instance, when a pregnant woman abuses drugs, her child is often born with health problems, and that's not a curse or a punishment, it's just the way things are. Some things are more subtle, like parents dying and leaving you with their debts to settle, parents doing bad things to you that leave you emotionally scarred, and so forth. In general, it's just a fact that people tend to follow in their parents' footsteps, and if you do something that you really ought not do, your children may be cursed for it not because God's angry at you, but because they decided to follow in your footsteps. This may not account for every instance on the page linked, but I think it accounts for a lot of them, and I'll discuss other ones when I get to them. In this case, it may be the fact that Ham's immoral act performed for Canaan to witness it may have led Canaan into a sinful life which in turn led his descendants into sinful ways of their own. So think about the example you set for your children, all you parents out there.