Measuring the mass of the W boson is an important check on the consistency of the Standard Model. The target precision for measurements of the W boson mass at the Large Hadron Collider is O(10 MeV), i.e. about 0.1 per mille. Achieving this degree of precision will require extremely good theoretical control on all aspects of vector boson production, including the simultaneous effects of QCD and electroweak corrections. I will describe a recent calculation of these mixed QCD-EW corrections to W and Z boson production, and discuss their impact on the measurement of the W boson mass.