Upcoming cosmological intensity mapping surveys will open new windows on the Universe, but they must first overcome a number of significant systematic effects, including polarization leakage. We present a formalism that uses scan strategy information to model the effect of different instrumental systematics on the recovered cosmological intensity signal for `single-dish' (autocorrelation) surveys. This modelling classifies different systematics according to their spin symmetry, making it particularly relevant for dealing with polarization leakage. We show how to use this formalism to calculate the expected contamination from different systematics as a function of the scanning strategy, and we comment on the extent to which changing the scanning strategy can mitigate the systematics. Most importantly, we show how systematics can be disentangled from the intensity signal based on their spin properties via map-making. We illustrate this for some simple instrumental systematics, demonstrating the ability to significantly reduce the contamination to the observed intensity signal. Crucially, unlike existing foreground removal techniques, this approach works for signals that are non-smooth in frequency, e.g. polarized foregrounds. These map-making approaches are simple to apply and represent an orthogonal and complementary approach to existing techniques for removing systematics from upcoming 21cm intensity mapping surveys.