English is only my second language, but based on this I would use 'do wrong' in the same way they are giving 'go wrong' as an example. Would that be wrong? Is it a rule or convention when it comes to this?
Apologies, my comment was somewhat discourteous, given the circumstances.
In "Do wrong", wrong is being used as a noun; it's the same construction as "Play cricket". The wording I questioned was "Do it wrong". That's the same as "Play cricket well". Cricket is being "played well", with "well qualifying "played" rather than "cricket". Similarly, "it" is being "done wrong".
Hence, "well" and "wrong" are being used as adverbs, each qualifying an action. However, the adverbial form is "wrongly", not "wrong".
Therefore, "Do wrong", but "Do it wrongly".
At least, that's my view. Not sure whether too many people care these days - simplification and all that...