When I was at school the external examinations we took were set by the Northern Universities Joint Matriculation Board, and that continued to be the case during much of my teaching career. I presume the Universities of Leeds, Liverpool, Manchester, Sheffield and Birmingham tried to cover their costs but I doubt if they tried to make much profit out of the operation.
I don't recall any great fusses abut errors and unanswerable questions, though occasionally the question papers were accompanied by a "correction" slip putting right some mistake in the printed paper. These caused no problems to those sitting the exam (indeed, the invigilators made such a performance of making sure everyone understood the correction that they gave us useful extra time to think) though they could cause a bit of a nuisance if the correction slip had been forgotten or misplaced when the papers were used in future years for examination preparation.
Now the examination boards have been merged and privatised and the media are full of a record number of errors and unanswerable questions. Presumably the errors are unspotted because the profit maximising boards are reluctant to incur the additional costs necessary for thorough checking. The deterioration in standards does not give much credence to the "market forces" mantra of private sector good public sector bad.
To be strictly fair public examinations are a much bigger and more highly publicised operation today than in the "good old days" when they covered a much smaller proportion of the population and examinations were more of a private matter between the student, parents and the teachers. Whilst having no wish to reduce the number of people gaining meaningful qualifications I do feel that the annual round of publicity is rather overdone, especially when, errors and omissions apart, it tends to be limited to moans that the standards of the students are are falling if the percentage passing falls, and the standards of the examinations are falling if the percentage passing rises.