Is anything inherently random? Is anything inherently random? Or is all randomness observed in data either "errors in measurement" or "lack of understanding"? Assume we could measure everything with infinite precision and had a complete understanding of all the deterministic processes. Would there be any process that would appear "random" in the data or would every dataset be deterministic at that point?

Yes, there are "inherently" random processes in the universe.  As far as I know, it's impossible to determine in advance the collapse of a wave function.  For example, which slit a particle will go through in the two slit experiment.
This question should really be asked on physics.stackexchange.
