This isn't strictly about slavery, but it mentions mental conditioning as a part of the process—part of how the peasants are enslaved is because they are brought up knowing nothing else. This also connects to the idea that life in the 6th century is a lot like life in the 19th century.
They were freemen, but they could not leave the estates of their lord or their bishop without his permission. (13.5)
There's some serious irony between the title freemen and how free these men actually are. Twain loved to use serious irony, but makes his point without a whole lot of snarking here. If you can't leave somewhere when you want to, it's pretty hard to call yourself free. The point pretty much makes its own gravy.
Any Established Church is an established crime, an established slave-pen. (16.2)
Pretty gutsy move here, equating the Catholic Church—and to some extent, organized religion in general—with a form of slavery. This kind of point would be right at home on a news show today, with some red-faced pundit in Shouty Man mode arguing either for or against the statement. Twain didn't have cable news though, and he expressed himself with a bit more elegance, but his point is just as blunt.
A master might kill his slave for nothing—for mere spite, malice, or to pass the time. (18.4)
This is like the idea of not being able to leave without permission. Twain puts his finger on a key part of what slavery is here: a life that the law considers worthless.
They had been heritors and subjects of cruelty and outrage so long that nothing could have startled them but a kindness. (19.4)
This could suggest a workday normality to slavery and oppression. Everyone's used to it, so they don't realize how wrong it is, and this reality puts Hank's task into stark relief. It's not enough for him to free everyone: he has to get the whole society to accept it and treat each other differently as a result.
One needs but to hear an aristocrat speak of the classes that are below him to recognize—and in but indifferently modified measure—the very air and tone of the actual slaveholder. (25.2)
This passage gets at the heart of the issue: Why, specifically, does slavery exist? Because some people think they're better than others. It's sad, but it happens time and again throughout human history. It's still around today, which just might be why people keep reading books like this one.
It reminded me of a time thirteen centuries away, when the "poor whites" of our South who were always despised and frequently insulted by the slave-lords around them, and who owed their base condition simply to the presence of slavery in their midst, were yet pusillanimously ready to side with the slave-lords in all political moves for the upholding and perpetuating of slavery. (30.10)
More philosophizing: Hank draws a direct link to the slavery of 19th century America, and also talks about how it causes people to work against their own best interests. The Civil War ended twenty years before Twain wrote the novel, but a lot of the issues it caused were still around, stinking up life for everyone: poverty, racism, and inequality, especially in the South.
SLAVES! The word had a new sound—and how unspeakably awful! (34.12)
It's never quite so bad until it happens to you, is it?
What Englishman was the most interested in the slavery question by that time? His grace the king! (34.2)
It takes actually being enslaved himself to get Arthur to see reason, suggesting that it's really hard to change people's minds sometimes. We can see similar behavior today when people talk about strongly held political beliefs—there's lots of yelling and screaming, even when they can't come up with a good reason to support their argument. Sometimes you've got to get cut yourself to realize that you can bleed, too.
Slavery was dead and gone; all men were equal before the law; taxation had been equalized. (40.2)
Hank really stresses the need to free everyone. This is his triumphant moment in the book, the champion's strut just before the big stumble. Twain lets us know exactly how important it is, and he even mentions it before discovering America in the paragraph so that we see it front and center.