I'm not so concerned about dead fish, as fish do die at LFS all the time, though places should remove them from tanks and not leave them in there all day. Fish do also get diseases, and since very few places QT their fish before they put them out, you're going to find some places having fish in their tank with ich and such. I think it's more important how the place acts when they see this, do they remove the fish and treat the system or just leave it there? This goes hand in hand with having a Knowledgeable staff.
Having knowledgeable staff is a good trait, not so much for me but for newer people that go to store. In the end a bigger issue would be if a store would sell something to a person that doesn't know how to keep it or sell them something that will not work in their tank, either a very hard to keep, a fish that is too large, or will be, for their system, or a fish that is going to kill all their other fish, just for the stake of making a sale.
I've never been concerned with a store looking neat and clean, especially concerning all the water on the floor and boxes, but for some people this is a big thing. I've know many people that will not going back to a place because it was a mess.
Rare and cool thing are probably what does it for me more than anything else, as well as having a lot of livestock to chose from. Prices can go hand and hand with what they have, though I do like places that will work with you.