  Without proper control of numerical and methodological errors in theoretical
predictions at the per mille level it is not possible to study the effect of
input parameters in current hadron-collider measurements at the required
precision. We present a new version of the parton-level code MCFM that achieves
this requirement through its highly-parallelized nature, significant
performance improvements and new features. An automatic differential cutoff
extrapolation is introduced to assess the cutoff dependence of all results,
thus ensuring their reliability and potentially improving fixed-cutoff results
by an order of magnitude. The efficient differential study of PDF uncertainties
and PDF set differences at NNLO, for multiple PDF sets simultaneously, is
achieved by exploiting correlations. We use these improvements to study
uncertainties and PDF sensitivity at NNLO, using 371 PDF set members. The work
described here permits NNLO studies that were previously prohibitively
expensive, and lays the groundwork necessary for a future implementation of
NNLO calculations with a jet at Born level in MCFM.
