How would BTC mining be different if the dif retargetted every block?

[mustyoshi]

Would the profitability of it change?

[litecoin_messiah]

Yes, There will also be many security issues relating to it.

[TierNolan]

Would the profitability of it change?

It would depend on how much smoothing happened.

Some alt coins retarget every block, but use the last 100-200 blocks rather than just the last block.

[softron]

Using everyblock would produce high diff flunctuations when big miners/pools go off/on that would not be good.