Let's say you want to pull a lever or open a chest, but enemy is hitting you with some pesky arrows that barely pierce your DR. Yet, this succesfully prevents you from doing that. Say, I've got a barbarian, I have more than 400 hitpoints at lvl13, yet attack that deals 1 damage after my DR is taken into account prevents me from opening the door. That's simply annoying. I believe many people face similar 'problem' sometimes, and I believe adding more use to Concentration would improve the gameplay.
List of actions that should continue on succesful concetration check just like spellcasting:
Pulling levers, switches, valves
Opening doors
Opening locks
Opening chests
Disabling devices
Using various quest thingies, like gongs
I think there might be some other actions that should be given concentration check as well, but I'll leave it open to public opinion.