looks as tho it happens a lot
https://www.gov.uk/correct-marriage-registration
If your parents turned up at a church or wherever and the priest went thro all the lardy-daah, and the registrar was there to record it all ( albeit wrongly ) ( adjust facts as needed, protestant, vicar, confetti etc )
then I think they have been legally married
whether or not the certificate mentions Miss pIggy and Kermit the Frog.
My father had a birth doc of some sort with name reversal - John Joe Smith instead of Joe John Smith, which had the British civil servants scribbing convulsively but it was all solved with an affidavit