I seem to recall (I could well be wrong) that the calculations for the Voyager space probes are all done using Newtonian mechanics. For something to be wrong implies to me that it is of no utility - which clearly isn't the case with Newtons work.

When you model some physical system you do it with and end in mind and a lot of assumptions have to be made (e.g. that gas flow is non-turbulent, heat flow is uniform) which are all wrong in some sense because reality isn't like that but if you didn't make these simplifying assumptions then you'd never get anything done.

Mathematical models aren't reality - they are an attempt to create structures that allow us to explain and predict and the assumptions underlying the mappings between these structures and reality are just as important as the contents of the theories themselves. It's possible to model the same system in umpteen different ways - indeed as there is no all encompassing theory-of-absolutely-everything you have to make some important decisions when you model something as to what is relevant. Trying to model plate tectonics in terms of string theory is unlikely to get you very far - that doesn't make string theory "wrong".