I could be wrong but I seem to recall that there is a ter'angreal in the Tower that is used to make the cloaks.

Elaida

Gawyn

Alviarin

Elaida, because she is just so stupid. This highly trained Aes Sedai who should at least have some clue about the liabilities of interpreting a Foretelling, should have half an idea just how much she is alienating the tower as Amyrlin, and hasn't the backbone to stand up to Alviarin's blackmail.

Gawyn lets a single rumor control him almost to exclusion of all else, and shows a talent for making truly terrible decisions.

I could have chosen several others for the last spot, whether Arymilla, or any of the various southern nobles for whom the only winning battle tactic is a cavalry charge to scatter the rabble, but Alviarin takes it for a level of incompetence not fitted to either of her offices.

Through all Randland, Light as well as Dark, it seems that "leadership" is based not so much on convincing others to follow you by persuasion and example, but rather browbeating those around you until they obey without question. While you could consider this a knock on the forces of Light, the followers of the Dark are even worse--at least the Light faction cooperates among themselves to drive back the Dark, whereas the darkfriends and Forsaken are all about personal power to the exclusion of everything else, at least when the Dark One isn't actually watching.

There are plenty of imperfections in the forces of Light, but the grass isn't even a pale green on the other side, it's completely withered.

I'm also new to Dragonmount. I'm just beginning my second full read-through of the series and there are no characters I can really say that I hate (though the behavior of some, especially Nynaeve, Elayne, and Egwene, grew a bit tiresome in some of the middle books). They tended to grow into better things though and by the time of the Last Battle I could call myself a fan of Egwene.

Two others, however, Elaida and Gawyn, take first place in annoyance for their stubborn refusal to see anything but their own world-views (that particular flaw is hardly unique to those two, but they take the prize due to the lack of evidence supporting, and the heap of contrary possibilities that they ignore).