Don't forget, Verin, according to her version (which her actions & information seem to support), only joined the Black to save her skin and tried to gather information on them and find a way out. When she was away from the rest of the Black Ajah and the Shadow's minions, as she was on her extended field trip into the boonies with Alanna, there would be no reason for her to act like a Black sister - she was not in it for power or greed or any other untoward motivation. Therefore, there would have been no behavior characteristic of Darkfriends or evil-minded people to tip Alanna off.

All such speculation regarding Verin is absurd. For Moiraine, or Alanna, or Rand & friends, or the Aiel or any other of her traveling companions to have suspected her based solely on the time spent in her company is ludicrous. Even my next iteration of "Egwene's evil" will not go so far as to accuse Egwene of not knowing better despite spend 4-6 months traveling in her company. The more logical and sensible form of this question to apply to Verin is "How did Liandrin & Alviarin and other Blacks of her aquaintance not notice that she was a/the Lightfriend?" And for that, the same principles would apply as in the case of other Darkfriends who flew under the radar, like Ingtar or Careane.