If Hegel relies on false observations about other cultures or false historical claims to make his arguments in the philosophy of history, then I would think that it would undermine those arguments. I suspect that those false claims do in fact serve as evidence for his views in the philosophy of history, which means that his views are indeed undermined.
But perhaps his false and distasteful historical and cultural claims are not meant as evidence for his theories, but illustrations of them. If so, then his claims are *again* weakened by his errors. For, if his theory makes predictions for phenomena that do not in fact obtain, then that would seem to suggest his theory is not satisfactory.
Finally, if his falsehoods are neither supporting his theories or supposed to stand as examples of the explanations those theories provide, then I suppose they would not weigh on his views, casting a bad light merely on his character.
But surely other readers of Hegel may disagree.