I wonder about these things too. Here are some of my less-than-comprehensive observations.

Characters with perception seem to find rings in campfires more often. It's trivial, but I am pretty. Pretty sure about this, that is. Oh, I'm not bragging. I am pretty, especially after I have been sobbing for hours about god-knows-what.

I also feel like I've noticed the chests are fuller when players have higher luck and/or perception. One game I had no perception on anyone and low luck, and the chests in the haunted house were almost empty, re-load after re-load. However, I usually have lots of luck and there is usually lots of treasure. Perhaps this is mere chance.

Perception will spot more secret doors if you don't know where they are already. It will also spot trap squares and help you dodge the traps, I think, but I might be wrong regarding the latter clause.

Also, it probably is best to wear Knights Boots as much as possible, because they are HOT. You know what I mean, mon frer d'fer.

Higher Luck in the party seems to help in Arcomage. And then of course there are the skill points from challenges, etc. Not to mention if you hang out a lot at Miners Only, Erathia's Finest men's bar.