With respect to procedures I find as a general rule the knowledge of what is in the POH is abysmally poor even among Instructors. A very real problem is “flight school-isms” .These are procedures that get mindlessly passed down from Chief Instructors to Instructors to Students without any critical thought and are often directly contrary to what is in the POH.
With respect to checklists the test should be. Will omitting or getting this action wrong significantly reduce flight safety. If the answer is no then it should not be on the checklist. I rewrote the checklist for a school I was helping out at. When I was done I removed about 50% of the items that were on the old checklist.