Is bitcoin mining itself compromising the security of SHA256
With a look up table you can avoid calculating the hash of a given input twice. Indeed, the block chain can be considered as a giant look up table, but one with very special forms of inputs: It links blocks and transactions to their hashes.

Though, why should someone choose a transaction or block as her password? Further, why would an attacker even try to look up a hash of a password in the block chain? He would have to assume in advance that the password is a transaction or a block (don't forget that even looking something up consumes some resources).