It came into my mind in the nick of time, how Columbus, or Cortez, or one of those people, played an eclipse as a saving trump once, on some savages, and I saw my chance. (5.6)
The incident with the eclipse sets the tone for the whole story: Hank has brains, which gives him an edge over a whole castle full of ignorant rubes. More importantly, he knows how to use his brains effectively. That's the difference between knowledge (there's gonna be an eclipse) and wisdom (I can pretend it's magic and scare the pants off of them).
Look at the opportunities here for a man of knowledge, brains, pluck, and enterprise to sail in and grow up with the country. (8.1)
Hank understands how much good he can do in Camelot. Why is that different than it would be in the 19th century? Possibly because so much of what he knows has already changed the country. Everyone's used to factories, electricity, and phones in the 19th century, but in Arthur's time—when it's all unknown—the impact is going to be much bigger.
Here I was, a giant among pigmies, a man among children, a master intelligence among intellectual moles (8.6)
Hank the Yank's not exactly a humble man when it comes to his brains, is he? Could that help explain why his accomplishments are undone in the finale? It certainly seems to set the hero up for the fall, which may mean that, while Hank has plenty of knowledge, his wisdom may be lagging behind a bit.
He was a darling; he was equal to anything; there wasn't anything he couldn't turn his hand to. (10.4)
Hank is talking about Clarence here, and specifically about his capabilities. Why does Hank struggle to educate and enlighten the other characters when Clarence betters himself so quickly? The cynical part of us thinks it was easier for Twain to handle the plot that way (since Clarence is basically Hank's Mini-Me), but it might also be evidence that Hank's task isn't hopeless, just very difficult.
I was training a crowd of ignorant folk into experts—experts in every sort of handiwork and scientific calling. These nurseries of mine went smoothly and privately along undisturbed in their obscure country retreats (10.1)
He's making people smarter… and yet he has to stay quiet about it. It speaks to a lot of the problems in Arthur's kingdom: fear and superstition, oppression, class warfare, and Merlin's general sneaky bastard tendencies. It also suggests that Hank needs to take his time in addressing them and move quietly lest he spook the herd.
Everybody swallowed these people's lies whole, and never asked a question of any sort or about anything. (11.1)
Knowledge and wisdom here comes from more than book learning. After all, curiosity—the ability to question what you're told—doesn't require an education. Hank's lament here is the lack of curiosity in the people. If you haven't seen a fire-breathing dragon, maybe you should look into their existence before freaking out about them…
These missionaries would gradually, and without creating suspicion or exciting alarm, introduce a rudimentary cleanliness among the nobility. (16.2)
Revolution through soap—go figure. Hank's plan is subtle and smart, and designed to keep his enemies in the Church ignorant to its true purpose. He's played this game before, and while it may fall on the sneaky end of wisdom, it certainly seems to work.
The "fountain" was an ordinary well, it had been dug in the ordinary way, and stoned up in the ordinary way. There was no miracle about it. (22.5)
Note that Hank fixes the fountain because he knows what the problem is, rather than explaining it through holy magic. Twain often debunks the more fantastical elements in Arthurian literature as simple ignorance, which Hank counters pretty easily with his just-plain-folks book learning.
"I've had the boys practicing this long time, privately; and just hungry for a chance to show off." (38.4)
Clarence surprises Hank with the knights on bicycles… proof that knowledge and wisdom aren't limited to just one man and can therefore be infused (by force if necessary) into the population at large.
This was not to be a duel between mere men, so to speak, but a duel between two mighty magicians; a duel not of muscle but of mind, not of human skill but of superhuman art and craft; a final struggle for supremacy between the two master enchanters of the age. (39.3)
Twain explains the stakes in the battle with Sir Sagramor, and weapons don't seem to enter into it. Enchanters in this case is a little misleading, though. While they both have their tricks, Hank's use real practical know-how—rope tricks actually work—while Merlin's are based on hogwash.
I suppressed the book and hanged the author. (40.2)
This is a joke from Twain—Hank hangs Sir Dinadan for writing a book of bad jokes—but it also suggests that Hank's dedication to free ideas is more self-serving than he lets on. As with earlier passages, Hank may be bright, but his wisdom sometimes lags behind.