The aim of this short note is: $(i)$ to report an error in \cite{Strat}; $(ii)$ to explain why the comparison result of \cite{Strat} lacks an hypothesis in the definition of subsolutions if we allow them to be discontinuous; $(iii)$~to describe a simple counter-example; $(iv)$ to show a simple way to correct this mistake, considering the classical Ishii's definition of viscosity solutions; $(v)$ finally, to prove that this modification actually fixes the the comparison and stability results of~\cite{Strat}.