Learn English – Why do we say “right-hand side”

In the phrase “to err on the side of…”, the meaning of err is closer to that of the Old French errer, which is “to stray”. The image implied is that, if you can't for sure walk on the right line, you might want to err on one particular side rather than the other.

So, just to make sure I answer your actual question: no, “to err on the side of…” does not indicate wrongdoing.

Yes, certainly.

Though you don't have to, as the writer demonstrates.

The credit/debit side and the good/bad part(s) are both fixed phrases with oppositions built in, and they oppose on the same semantic axis GOOD ⟷ BAD.

On the credit/debit side refers to double-entry bookkeeping, and is part of a metaphor theme that equates having money (credit) with GOOD, and owing money (debt, or debit) with BAD.

So they can be used pretty much interchangeably, as far as meaning is concerned.
In style, however, they're different, because one's metaphoric and the other's not. This may or may not matter to you.