  We review the experimental methods to measure mixing and time-dependent
$C\!P$ violation in $D^0$ decays into two hadrons. While these phenomena are
usually neglected for $D^0 \to K^- \pi^+$ decays, this approximation is not
always justified. In particular, it produces a bias on the measurement of the
parameter $y_{CP}$, when this is performed by relying on $D^0 \to K^- \pi^+$
decays as a normalisation channel, whose size is around 40% of the precision of
the current world average. Finally, we estimate the sensitivity to the weak
mixing phases achievable by studying $D^0 \to K^- \pi^+$ and untagged $D \to
K^- \pi^+$ decays, where $D$ stands for either of the $D^0$ and $\bar{D}^0$
mesons. Contrary to Cabibbo-suppressed $D^0 \to h^+ h^-$ decays, these decay
channels allow to measure these phases without final-state dependent nuisance
contributions from the decay amplitudes, but their sensitivity is lower by a
factor of six.
