Rather interchangeable, although there's a common belief that 'dużo' has to be used with uncountable nouns and 'wiele' with countable ones. In fact, it doesn't have to be like that. However, it's possible to use 'dużo' only in Nominative, Accusative and sometimes in Genitive, as it doesn't undergo declension. 'Wiele' officially doesn't have a Nominative, but can be used in all other cases (see here)

Well, first of all, the Nominative form is "błąd", even if most of the forms have ę and not ą (declension here).

I'd say that in everyday's speech they're rather interchangeable. I guess 'pomyłka' may be in fact smaller than 'błąd', but that's not in the definition. But "Zrobiłeś wiele pomyłek" sounds somehow strange to me. The collocation used with "pomyłka" is usually "popełnić pomyłkę" ('popełnić' is mostly translated as 'to commit'. Also it's quite possible as a collocation with 'błąd'). But still, if anything, I'd say "Pomyliłeś się wielokrotnie/wiele razy", turning pomyłka into "pomylić się" (to make a mistake, perfective) and adding "many times".

As far as I remember, in linguistics, especially in theory of learning languages, "błąd" (error) is when you use some form because you think it is correct - but it's not; and "pomyłka" (mistake) is when you use a form correctly usually, but sometimes make a mistake because of different factors.

True, it makes sense. Added now.