incompetence 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 competence.
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 physical or intellectual ability or qualifications
inability of a part or organ to function properly
Synonyms, antonyms and the broader and narrower relations for incompetence come from Princeton University’s WordNet. Full sources and licences.