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Cosmological parameter estimation from forthcoming experiments promise toreach much greater precision than current constraints. As statistical errorsshrink, the required control over systematic errors increases. Therefore,models or approximations that were sufficiently accurate so far, may introducesignificant systematic biases in the parameter best-fit values and jeopardizethe robustness of cosmological analyses. We present a general expression toestimate a priori the systematic error introduced in parameter inference due tothe use of insufficiently good approximations in the computation of theobservable of interest or the assumption of an incorrect underlying model.Although this methodology can be applied to measurements of any scientificfield, we illustrate its power by studying the effect of modeling the angulargalaxy power spectrum incorrectly. We also introduce Multi_CLASS, a new, publicmodification of the Boltzmann code CLASS, which includes the possibility tocompute angular cross-power spectra for two different tracers. We find thatsignificant biases in most of the cosmological parameters are introduced if oneassumes the Limber approximation or neglects lensing magnification in moderngalaxy survey analyses, and the effect is in general larger for themulti-tracer case, especially for the parameter controlling primordialnon-Gaussianity of the local type, $f_{\rm NL}$.

Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters