I haven't quite figured that out myself.  I've never looked at my completion % for a level after I've finished one, so i'm not entirely sure if it goes up or not.  I think it's more a matter of getting the bandages out of those levels or unlocking characters more than anything else.

There's an icon next to where the Warpzone's name is displayed that tells you if you've collected the bandages in there. That's the only way to know, as far as I'm concerned.

I was wondering this myself. Seems a bit sloppy compared to how good and clean the rest of the menus is.

Yeah. You just have to look up how many bandages are supposed to be in each warp zone and see how many are shown. I agree it's pretty sloppy to force somebody to use the internet to find out if they need to play it again.

WAAARRRPPP ZOONNNNEEEEE!!!