Having found this site useful, and having just won our appeal, please permit me to put some thoughts back from my experience.
The appeal hearing
Despite everyone trying to be nice - it is stressful (and I am an experienced public speaker, so trust me on this)
At the end of the hearing you will have no inkling which way it will go (this surprised me)
Before the day
Have a written scripted speech - you don't have to stick to it, but under stress your mind will probably go blank and you will miss making your main point (this is a critical point - I am an experienced speaker and I was mighty glad I had a script!)
Plan out what questions they might ask and make a list of the answers as you won't remember them on the day
For us these questions were:
Was he upset on getting the results?
What streams is he in in school - if he is not in the top stream why not?
Did he do any practice papers before hand?
Did he finish all the questions in the test?
Did he find one test harder than the other?
If he has some difficulties (special circumstances) will they hinder him at grammar school (I thought this question was a bit borderline)?
Write of list of all the things he / she enjoys eg:
What are the last 5 books he/she read?
What don't they like?
What do they watch on TV?
Although its difficult to tell I do feel that independent evidence is absolutely vital to backup all your arguements
Include press articles on say the impact of a special circumstance
Letters - especially from teachers
You should be able to back up every assertion you make with a piece of independent evidence - think court of law
If you are unsure of whether to submit the evidence in advance (and you must send most of it this way) take it with you - they will accept documents that you pass across the table (we did this)
Criticise the 11+ system - we all know it is flawed
Try to second guess where their questions will go - be prepared for them to delve into a point that you didnt think important at all - overprepare
Dyspraxia was one of ours - I think that we were lucky as one of the panel was very experienced in dyspraxia and it is a difficult concept to explain. It was difficult to see what weight they applied to it, but most of the questioning was around dyspraxia
They also had clearly read the papers in advance and had done some research of their own into some of the circumstances - assume that they will do this.
Keep it in proportion
Most grammar counties (this was Bucks) have excellent non grammar schools as well - so the outcome of a failed appeal is that your child will probably go to an excellent school - its just not a grammar.
Anyway - bit of a brain dump - but perhaps someone will find something of use - Good luck with your appeal.