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?
Nothing is ever stated in the books prior to her being raised, but she probably wasn't Keeper since we know Duhara was Keeper until Marith Jaen was raised in 984 and she most likely wouldn't have raised Siuan given that she had been in retirement for nearly the entire time Siuan had been in the Tower and reportedly disliked Tamra ... Siuan's being one of Tamra's favorites wouldn't have likely been a good reference for Siuan. Also Marith was quite old (284 when raised) so it seems unlikely she would have raised a very young woman as her Keeper. Also seems unlikely that Siuan being Keeper would have been left unstated. More likely she could have held one of the vague administrative roles assigned to running part of Tar Valon. Or was just spoken of highly by the Blues in the Hall.
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?
This is pretty much the side plot assigned to Cadsuane during New Spring. She reference the "vileness" in the main series, but during New Spring she was actively chasing down the Black which is why she took such an interest in Moiraine's activities.
Was Bornhald there? Fain had his own little cadre of White Cloaks he had infected with his evil, but I'm not remembering if Birnhald was actually with them when Perrins family was murdered ... He hated Fain IIRC ... Guess I need a re-read 
