On this page of our guide to Psychonauts 2 we've listed the Nuggets of Wisdom available in Compton's Cookoff.
There are 2 Nuggets of Wisdom in this level.
Nugget of Wisdom 1
Location Round 1.
It's pretty easy to get. You need to jump off of the pan to the red railing, then jump to the correct fragment. This task shouldn't pose a problem.
2nd Nugget of Wisdom
This secret can be found only when revisiting the stage. You must first develop the Mental Connection.