I've tried getting bills that is missing a small piece of the corner and that is not accepted. But some of the really dirty ones, as long as nothing is missing is fine. I refuse them if they are 50 or above and not in good shape. I'd rather have a stack of old dirty 1's than a 50 that cannot be used. 

Technically the banks should accept any bill as long as they are not counterfeit, but I've heard people say even banks refuse. 

Fear flashes through me every time I have to touch Chinese money.  It's the most unhygienic currency in the world.

Because my employer refuses to deposit my salary into the bank, I receive cash.

Because of my money handling phobia, I stopped counting it each month when being paid.  

Because the finance officer is an opportunistic, thieving bastard I was short changed by several thousand yuan.

Because Chinese people are subject to adverse social norms the theft can only be addressed as a misunderstanding.  And because of this, so say all of us!

I never understood why stores will not take damaged money that did come from an ATM. I have to go to the bank and they easily exchange it.

Just go to the bank and deposit it. It is their job to take those bills out of circulation. 

Any form of currency only has value if someone else thinks it has value and is willing to trade you something for it.  Does not matter if it is new or old and torn, made of paper or made of platinum. It is always only worth what someone else is willing to give you for it.  So no I don't care what it looks like, I only care who controls the amount of it in circulation.