This is a really well written paper. I especially like their review of Heisenberg's original uncertainty relation, which had already been shown to be incorrect in theory under certain conditions, and the modern uncertainty principle that still holds. (They then experimentally violate the former, not the latter.)

Why should anyone care? Well, some security proofs for quantum cryptographical systems out there could conceivably assume the original relation holds, and would therefore require correction. Not to go into too much detail, this might have an impact on the bit-rate that some quantum crypto systems can securely run at.