Just something off the top of my head:
What accolades did Siuan have to become the Amyrlin, besides her youth? Leading the Blue spies would have been a secret position, so how did she make her name? Was she the Keeper for the previous Blue Amyrlin?
Cadsuane thinks that in the past, she came close to uprooting the Black ajah. What was up with that? Was it related to the illegal gentling of male channelers, or maybe Sierin Vayu's death?
What was up with the utterly retarded trial between Perrin and the Whitecloacks in ToM? I know Perrin is an idiot, but surely RJ couldn't have planned such a plot? And how did nobody point out that the main accuser, Dain Bornhald, was responsible for the death of Perrin Mom, Dad, sisters and kid brother?