[HarHarVeryFunny]

The catch/lifting points may look small, but actually protrude from the side of the booster by 2-3 feet. Note that the booster is actually in a hover at the point the arms close in to touch it, so as long as it's vertical rotational axis is right (there are only 2 pins - one on either side), the positioning of the pins on the catching arms is basically guaranteed.

[cryptonector]

Right, so if SpaceX meant that they had an error of only .5cm maybe they meant that the error on the booster rotation angle was small enough to produce only a .5cm error at the catch points. Since they weren't specific, it's hard to know what they meant.

The booster rotation angle error and the catch point placement error were much too small to detect with the naked eye on the published videos. Every other measure of accuracy was clearly within tolerances -- and also hard to discern with the naked eye.

As amazing as .5cm accuracy sounds, if SpaceX meant catch point placement error, then it's quite as impressive because that only implies everything was within tolerance _and_ only the booster rotation angle error need have been impressively near-zero measure. That's... still amazing, honestly. If you can get the booster rotation angle error near zero then you can get the other errors way down too.