If a man and women find out there was a mistake in their Nikah (out of ignorance) and they already had sexual intercourse. Is iddah needed to be observed before correctly reading the Nikah again?
Chapter twenty-nine » Miscellaneous rulings on divorce Ruling 2554. If a man has sexual intercourse with a woman who is not his wife supposing that she was his wife, the woman must observe ʿiddah, irrespective of whether she knew that he was not her husband or supposed that he was her husband.
No. Ruling 2554 talks about a woman who is married to another man. In your case, the sexual relation was with the same man, and it was not fornicate. Hence, there is no need for iddah.