Pitch error with ground ballscrews is measured in microns. Moreover, the good ones come with charts showing the measured errors, so software can correct for even that tiny bit.
One "problem" with ballscrews is that they offer very little resistance to movement. Thus, force applied to the "nut" can turn the screw quite easily. In good designs, that is not a problem, but in some DIY applications it can be. One example is the retrofitting of a Bridgeport-type mill with ballscrews for hand operation (rather than stepper or servo for full CNC). People who have done that have found that while precision of positioning is initially great, during the course of a cut, the workpiece may make the table move.
0.01 mm is about "4 tenths" , i.e., 0.0004". That level of accuracy is relatively easy to attain today. Even some conventional leadscrew/bronze nut designs can achieve that level.
John