But with this scene, I got the impression that it was almost code word territory, so with Saerin's comment the others stood up knowing it would benefit Egwene (as it was Egwene's allies within the Hall doing this), preventing the rest of the Hall looking further into it.

I.e. Saerin at least knew what the consequences would be, possibly still under the delusion that it was best for Egwene to deal with the Dragon.

EDIT: though I do have to agree with your general comment regarding intelligence drops across the characters, Mat was the most painfully obvious, but there were many painful points.
And I also think that when Rand says that Moridin thought he was the Dark One at one point, to which he agreed, doesn't seem to agree with the actual text of the first 3 books (such as where Ishamael said Rand gave him too much credit when calling him the Dark One).