We have controlled to sub-4% the (known) systematic biases in the ensemble weak-lensing mass calibration of galaxy clusters at low redshift (arXiv:1507.04493, 1507.04376), and controlled XMM/Chandra cross-calibration systematics to a similar level (Martino et al. 2014, MNRAS, 443, 2342). I will summarize key features of our analysis that enable this level of accuracy, and present new accurate tests of hydrostatic equilibrium in clusters at z=0.2 (Smith et al. 2016, MNRAS, 456, L74). I will also discuss implications for clusters as a cosmology probe, focusing on the ongoing tension between Planck's primary CMB and galaxy cluster-based measurements of sigma-8.