Quote 1
"We do not know if, out on the moons of Saturn, you will meet with good or with evil—or only with ruins a thousand times older than Troy." (30.23)
Heywood Floyd compares the possible alien ruins to the ruined city of ancient Greece. It's hard to imagine that anyone would actually say something like this; it sounds like something you'd read from a script. But it's thrown in there for the same reason the novel is called "A Space Odyssey"—to reference other old, important, impressive stories and make the events here seem important and impressive.
Quote 2
"…primitive races have often failed to survive the encounter with higher civilizations. Anthropologists talk of 'cultural shock': we may have to prepare the entire human race for such a shock." (30.210)
These days, anthropologists try to avoid talking about "primitive races" or "higher civilizations". Cultures with stone-age technology aren't necessarily backwards, nor are they fossil relics. In some ways some of those cultures might be seen as more advanced than highly technological ones (in terms of equitable distribution of goods, for example, or in terms of richness of interpersonal relations). This speech about "primitive races" is supposed to sound scientific and rational and modern, but it actually sounds kind of prejudiced and out of date. That's the danger with science-fiction; your future is always at risk of looking quaint and old-fashioned.
Quote 3
"Thank you," said Floyd with a smile, wondering why stewardesses always had to sound like robot tour guides. (7.24)
Even in the future, the stewardesses are all women. Floyd wonders why she has to sound like a robot—but the answer is that she, like all the women in the book, doesn't get to be a real person, she's just window-dressing.