The main point is the uncertainties are underestimated, cause you can confuse a heavier Z boson for a W if one of the muons to which Z decays escape detection and so the event looks like a muon-neutrino decay of Z. The author seems to doubt that the way the data is corrected for this is really that precise.
And he also seems to imply that the LHC groups could do significantly better than they have to this point.