These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ensemble Dark Horse: Despite appearing in only a few scenes, the Horned King was notable enough to be promoted into Big Bad in the adaptation of the second book
Fridge Logic: Okay. Dyrnwyn can kill the Cauldron-Born. Why did Gwydion not twig onto this while he had it in his possession?
Taran tried using it on the Horned King. The sword was too dangerous to use at the time.
Also, how often do you try to stab things that you know can't be harmed? Bear in mind that they hadn't read the full version of Dyrnwyn's runes yet.
Most importantly, the Cauldron-Born haven't been around since the second book since Arawn has been holding them in reserve now that he has a limited supply of them. The fact that they get weaker and slower the longer/further they are from Annuvin also makes them far more effective as guards than an assault force.
And note that when Arawn is ready to use them, the first thing he does is steal the blade. And after using them, he immediately has them head for home.
Jerkass Woobie: Ellidyr. He spends pretty much the entire book being a jerk to everyone, but especially heaps scorn on Taran, going so far as to drag him bodily across Caer Dalben and take it for granted that Dalben would punish Taran for "impertinently" backtalking a prince. This reaches new levels around the climax, when Ellidyr uses the heroes' desperation to bring the Black Cauldron to Caer Dalben as leverage to force Taran into agreeing to basically act as his servant and pretend that Ellidyr was the one who found the Cauldron (which is doubly cruel considering that Taran only got the Cauldron himself by giving up a brooch that his dead friend bequeathed to him). When they all agree to these terms, Ellidyr goes on to lose his mind and try to kill them anyway, somehow convinced that they were going to double-cross him. However over the course of the story, it's revealed that he's such a jerk because his family squandered their title of nobility and fortune, leaving him with virtually nothing but his title as a prince and his ill-tempered horse. He also ends up severely beaten and taken prisoner while trying to bring the Cauldron back to Caer Dalben, and is horribly broken when he is unable to even free himself to save the group from death. He ends up throwing himself into the Cauldron at the cost of his own life because that's the only thing he can do to help the others, and does so after swearing "on what little honor [he] has left" that he only wanted the Cauldron destroyed, and never intended to use it himself.
To make it even more of a Tear Jerker, said ill-tempered horse deliberately runs off a cliff in anguish at Ellidyr's death.
Nightmare Fuel: Reading the final book, it seems that at least part of why actual displays of full-force magic are so rare in the series is that Prydain-style spellcasting results in this when fully unleashed.
Tear Jerker: A half dozen in the last book, easily. A very brief list - Coll's death far from home in a barren wasteland, Prince Rhun's death, Fflewdur Fflam destroys his beloved harp and has to leave Prydain forever, Doli and the Fair Folk leave the surface world, Gurgi has to go back to the Summer Country with the Sons of Don...