I fitted thousand of linear regression models and I corrected the p-values of the beta coefficients for multiple testing. When it's time to test goodness of fit of these models (normality, heteroskedasticity, lack of fit), does multiplicity come to play? What I am doing is Kolmogorv-Smirnov to test normality of the residuals of each model, does it make sense to adjust p-values for multiple testing to maintain 5% FWER? In this case a type II error is worse than a Type I error, specially in testing heteroskedasticity or lack-of-fit test. Thanks!
No, because p values aren't really the point of goodness of fit testing. The reason you test goodness of fit (e.g. here, that the residuals are normal) is that, if they are not, it violates an assumption of the model.
So, the key point is not whether the non-normality is significant, but whether it is large enough to invalidate any conclusions you might make from the model.
Much better to look at quantile normal plots.