I didn't think of this myself, but someone else did some speculating here:
1) Pemulis is supposed to be waiting to find out how much trouble he is in over the Eschaton debacle outside CT's office 2) He seems to be aware that something is up in Avril's office, and drops in for the purpose of telling Avril that he knows that she is fooling around with John Wayne. 3) He is figuring that Avril won't let him get kicked out of school given what Pemulis knows, i.e. he is kind of blackmailing her.
Also, this scene is analagous to the one in Hamlet when Hamlet kisses his mother, Gertrude, full on the lips, and Polonius is secretly watching from behind the curtain. John Wayne is wearing Orin's football uniform in this scene, so there is something just a little incestuous going on (and Avril is dressed like a cheerleader?!! WTF?!!) I think it's pretty established that Pemulis is analagous to Polonius, the supposed smart guy who is actually a fool, because he lacks wisdom.
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