incorrectness has 1 distinct synonym spread across 1 of its 2 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is correctness.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
lack of conformity to social expectations
the quality of not conforming to fact or truth
Synonyms, antonyms and the broader and narrower relations for incorrectness come from Princeton University’s WordNet. Full sources and licences.