There are dialects that are non-standard but are dialects nonetheless.
I don't know whether "He don't know nothing" fits the established syntax of a dialect or not. You can't take an isolated sentence and ask it it's part of a dialect. It could be a mistake, or it could be part of a regular pattern of double negatives used by a group of people as one of many unwritten but universally used set of language "rules" that mean it's a dialect.
It's a non-standard form that occurs in many different regional varieties, so in those contexts it is. I'm not sure that all "bad" English would fit the dialect description- slang, for instance, may use non-standard language without necessarily belonging to a dialect.
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