[Xaccers]

If the school noticed his lack of appropriate shoes before the exams and did nothing, but then decided to send him home 20 mins before the start of an exam, that is totally wrong.
However, even if they turned a blind eye to it, but then sent out a reminder to all pupils that they were to wear appropriate shoes for the exams, then they are entitled to do this, although I still think he should have been given a warning rather than made to miss the exam.

Something tells me we aren't getting the whole story here from both sides.
It could be that he was looking at a fail anyway, and excluding him from the exam would be marked as a no-show rather than lowering the schools grades (assuming that in secondary schools that is the case with the results)
At my school, several years after I left, pupils had to re-take an exam because the average grade was so low.
They had to do this after school and what ever result they achieved it would not change the original one.
It was simply a punishment from the head for the pupils low interest in the subject