Learn Polish: Zrobiłem supeł, ale mimo wszystko dziergam dalej. - I made a knot, but despite everything I keep knitting.

You are exactly right that mimo (and pomimo) generally require the genitive case, like in mimo deszczu (despite the rain). However, there is a fixed exception: when followed by the pronouns to or wszystko, they take the accusative case instead. That is why we say mimo wszystko (despite everything) and mimo to (despite that).

How does dalej translate to "keep" in dziergam dalej?

Dalej literally means "further". In Polish, adding dalej after an imperfective verb is the most natural way to say "to continue doing something" or "to keep doing something". So, dziergam dalej literally translates to "I knit further", meaning "I keep knitting".

Why do we mix the perfective zrobiłem with the imperfective dziergam here?

The aspects perfectly map out the timeline of events. Zrobiłem is perfective past because making the knot was a completed, one-time event (likely an accident that already happened). Dziergam is imperfective present because the knitting is an ongoing, continuous action happening right now, continuing in spite of the mistake.

Could I use węzeł instead of supeł for "knot" in this context?