irregularity has 4 distinct synonyms spread across 4 of its 4 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 regularity.
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.
behavior that breaches the rule or etiquette or custom or morality
not characterized by a fixed principle or rate; at irregular intervals
an irregular asymmetry in shape; an irregular spatial pattern
irregular and infrequent or difficult evacuation of the bowels; can be a symptom of intestinal obstruction or diverticulitis
Synonyms, antonyms and the broader and narrower relations for irregularity come from Princeton University’s WordNet. Full sources and licences.