The "Blind Idiot" Translation of Dyrnwyn's sword. "Draw Dyrnwyn, only thou of royal blood." Eilonwy said that it didn't literally mean king's blood, but she couldn't explain what it meant, and Gwydion later said it meant "noble worth." It's likely that the first term was a metaphor for the second, and Eilonwy couldn't explain it properly because metaphors and idioms don't always translate well.
Why does Taran get over his Aesop Amnesia after Book 2? One of the reasons is that in The Book of Three, everyone comes out as well as, if not better, than they started out — he's honored and becomes friends with Gwydion, Doli Took a Level in Kindness and gains the power of invisibility, Eilonwy now has friends and a home, Gwydion gets the ability to talk to animals, etc. However, The Black Cauldron involves Ellidyr and Adaon making a Heroic Sacrifice, and Taran giving up the brooch which meant so much to him. He's learned the real cost of adventures.
Not only that, but in Ellidyr he saw exactly what happens when you get too obsessed with glory and honor.
Furthermore, his near-terminal obliviousness towards Eilonwy in Book 5 may well not have (entirely) been his being clueless. At a couple of points, he seems on the verge of proposing, but seems to have decided not to do it in the middle of a war. In fact, it's all but stated that he had wanted to propose to her at the very beginning, but then Arawn rudely interfered by luring Gwydion into a trap.
The bit about Taran not being able to draw Dyrnwyn because he's not of royal blood? "Blind Idiot" Translation issue aside, Book 5 reveals that we don't know who his parents were. For all we know, he could be of royal blood.
A small (though no less meaningful) moment in book 4: the finding of Morda's Soul Jar. It seems to happen by Contrived Coincidence, thanks to Kaw getting playful with Fflewddur's harp key (after yet another mishap with the strings), followed by Gurgi, resident finder-of-things, climbing the tree. Certainly possible, considering the crow's trickster nature. But then, after Fflewddur convinces Taran to have Gurgi put the coffer and bone back in the tree, they encounter the transformed Doli—and while it's told in retrospect, Taran notes that's right when Kaw flew back and disappeared, only to show up on the way to Morda's lair with the bone. Kaw didn't get to hear Doli's story, but consider: while he seems to be a normal crow (other than his minimal ability to talk), he dwelled with Gwystyl for some years beforehand and generally seemed to have been part of the Fair Folk's doings. So there's a very good chance he's able to sense and recognize magic, like the bone. Even without that, the fact Doli had just been found transformed (when that shouldn't be possible) would have warned Kaw that magic was afoot. And eventually Morda reveals that his ability to place his life in a Soul Jar came from Angharad's amulet...which Doli in turn reveals was a wedding gift to her mother from the Fair Folk. So whether magic in general or Fair Folk magic in particular, there's a very good chance that the clever Kaw put two and two together and realized the bone's importance, if not its specific nature. So whether or not the original discovery was a coincidence, his return to fetch the bone was clearly not the Attention Deficit... Ooh, Shiny! moment Taran assumed it to be.
Dallben's use of both The Book of Three and his caretaking of Hen Wen is actually a brilliant method of staying as informed as possible. Not only is Hen Wen herself an "oracular pig" whose power of prophecy seems to always be accurate (if infuriatingly vague), the Book of Three being revealed to cover the events of every possible timeline, its usefulness severely limited by the sheer volume of information, and only some of it being accurate. Since both forms of foresight are vague in completely different ways, combining them together would give Dallben a much better idea of the immediate future than either would in isolation.
Additionally, by staying at Caer Dallben he's able to keep both safe from Arawn, his agents, and anyone else who might be too nosy for their own good. The brilliance of staying on a farm is also notable: Castles constantly have lots of people wandering in and out and all around, but on the farm he can easily keep an eye on everything and everyone who comes and goes. Having a retired but still expert warrior around to do the work and keep an eye on things doesn't hurt either.
Okay. Dyrnwyn can kill the Cauldron-Born. Why did Gwydion not twig onto this while he had it in his possession?
Maybe he never fought the Cauldron-Born between Books 1 and 5. Yes, he's the Hero of Another Story, to be sure, but since they can't be killed, he may have just hidden or run from them whenever he encountered them (which would make sense, because why would you go up against a Cauldron-Born if you had any other option?). I admit it's a bit flimsy, but can't think of anything better.
Alternatively, it may have been destined for a worthy user, specifically Taran.
We don't really see the Cauldron-Born at all during this time, likely because Arawn became aware that Dyrnwyn had been found, and was keeping his troops away from it. Along with the fact that the Cauldron-Born slowly lose their power the longer and farther away from Annuvin they are, the loss of the Black Cauldron, in the second book, provided a perfect excuse to keep them under cover. Since he couldn't make more of them, he was keeping them close so as not to lose any (even a deathless warrior could be hacked to pieces).
Plus, it's not that he spends all his time wandering around the country, either—while he does have lots of adventures, he also spends lots of time at Caer Dallben and Caer Dathyl, and there was that stint on Mona.
