There are two separate issues here.1. Maladministration
For appeal purposes, maladministration tends to mean more than 'something was done incorrectly'. The issue is whether you have therefore been deprived of a place to which you would otherwise have been entitled.
I don't know what the admission arrangements for this school are. Are places awarded in score order? If
so, and if
the child in question gained a place, and if
your child would have been next in line, then there could be an argument that you've been deprived of a place.
My advice at the moment would be to tread cautiously. Unless maladministration can be established, I wouldn't make it part of your case, or it could turn into a distraction, taking attention away from the rest of your case.
After the school has presented its case, there will be an opportunity for questions. My suggestion would be to refer to the incident at this point, to ask what steps were taken to ensure that the pupil in question was not placed at an advantage, and whether any other pupil or pupils could have been disadvantaged.
In other words, in the first instance you just try to establish the facts.2. Extenuating circumstances
What occurred might help explain an underperformance in the test. It depends whether your son's medical condition could reasonably be said to have been affected by the disturbances.
possibly as a result of the above issues
If the connection is tenuous, don't overplay it! Just a sentence will suffice.
start talking about "possibilities", it might count for little.
Something in writing from the GP and consultant about a possible impact would carry more weight. The evidence could then speak for itself.