correct has 19 distinct synonyms spread across 11 of its 12 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 2 recorded opposites are falsify, incorrect.
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.
make reparations or amends for
“right a wrongs done to the victims of the Holocaust”
adjust for
“engineers will work to correct the effects or air resistance”
punish in order to gain control or enforce obedience
“The teacher disciplined the pupils rather frequently”
treat a defect
“The new contact lenses will correct for his myopia”
in accord with accepted standards of usage or procedure
“what's the right word for this?”
Synonyms, antonyms and the broader and narrower relations for correct come from Princeton University’s WordNet. Full sources and licences.