This shouldn't be so complicated. I'm only referencing "NOTCHED INNER COVERS" not any other kind of inner cover, there are several designs. Some have flat sides (I got rid of mine), some already have notches, some are wood, some are poly...etc...
HOWEVER; If using a "notched" inner cover as a top entrance or vent opening the notched end should be DOWN. Always DOWN. By turning the notch up 'you' force bees to enter the hive through the center hole of the inner cover. That serves no purpose. In fact it kinda negates the purpose of an inner cover, no?
A little bur comb on the bottom of inner covers should be (is) expected, it doesn't bother me or my bees. Regular inspections keep things from getting 'mucked' up ;)