OK, we're talking about stage 1 of an oversubscription appeal where the admission authority has to satisfy the panel that the admission of another pupil will cause prejudice.
In the vast majority of cases the admission authority wins stage 1, and I think it's much better for parents to focus on stage 2.
Attacking the authority at stage 1 can descend into "nitpicking" and may not make a good impression.
No reason for not asking polite questions, however.
Most questions probably have to do with how many children can be fitted in a room, extra building work, or how well the school has coped with additional bodies in the past.
See the Q&As, end of C6, C8, C13, C14.