Funny, I was had janitor in mind when I posted, but I figured I would get more in depth conversations with workers if I was also out on the floor occasionally doing maintenance type as well.
The part is true what you say about respect and doing menial tasks. When I was doing some regional protective work, and there was time, I would do tasks that had been relegated a couple levels down. The new people were very surprised to see this, and commented about it. Of course it also was a two way street, as it gave me an opportunity to jump people's butts when on range day the boss is loading steel targets, etc into vehicles, and guys are standing around with cups of coffee in their hands.
Bottom line is a boss should never ask someone to do a job he is not willing to do himself. Nobody is so important that they cannot push a broom or take out the trash.