What would catastrophically go wrong if it was off by 0.1%?
Space shuttle/ rocket part dimensional accuracy
The thing that the world uses as a standard for the kilogram
The position of Stevie Wonder's piano
Our DNA pattern? Might need to be a bit more than that for things to go catastrophically wrong [for us].
Many of the constants in nature would let our world end in flames if changed a wee bit.
The fine-structure constant
Space shuttle launches?