Factual error: In the scene where Joe Clark and the Vice Principal go to the project buildings to see the young girl's mother, they walk down a short ramp to an apartment. Those project buildings are in Paterson,N.J. (where the story takes place), but walking down that ramp takes you to the boiler room, not an apartment. None of those buildings have apartments like that.
Factual error: Just after the opening credits, Thomas Sams is stuffed into a locker by two other boys, but a big kid like Sams would never fit into a real high school locker.
Factual error: The dates used in the movie were inaccurate. For starters, in the auditorium scene, Joe Clark said that the minimum basic skills test would take place on April 17. April 17, 1988 was on a Sunday. Also, when they did the countdown, 99 days before that date would have been Saturday January 9 (they couldn't have updated the sign). And in the scene when Ms Levias is yelling at Joe Clark, she said 'for the past 7 months' - it was only April, but he came in October (6 months earlier).
Chosen answer: They are discussing some of the things that Mr. Clark has done that has "embarassed" the school. They are debating what to do about him. And by "posturing," they mean his insistance on wearing African dress and espousing his political beliefs.