We report on ferroelectric behavior in wurtzite $\mathrm{Z}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{O}$ thin films across the accessible Mg concentration range. We outline a sputter deposition process for $\mathrm{Z}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{O}$ thin films using an oxygen/ozone environment to reduce electronic defects that limit insulation resistance. This procedure yields films that support ferroelectric hysteresis in Mg-substitution concentrations between $\ensuremath{\sim}8\phantom{\rule{0.28em}{0ex}}\mathrm{mol}%$ and 55 mol%. Generally, the remnant polarization has a modest composition dependence and all films show complete ferroelectric wakeup. Coercive fields initially fall with increasing Mg fraction and then increase above $\ensuremath{\sim}13\phantom{\rule{0.28em}{0ex}}\mathrm{mol}%$. The initial reduction is likely associated with structural softening via Mg substitution while the increase is likely associated with increased crystallographic disorder. The most resistive films reside in the 25--38 mol% Mg window. Electron microscopy reveals large stacking fault concentrations in as-deposited film microstructures consistent with sputtered ZnO. Chemical analysis suggests uniform Mg distribution in all films. For the test case in the Mg-rich regime, films become less resistive with decreasing thickness, but hysteresis is observable in a 66 nm layer.