Kimmy - Another panel member and chair here. I'd also second everything Admission and Positive Attitude have said.
Talking generally, the main no-no (in my view) is telling the panel that your child is such a prodigy that only the best school in the borough is good enough. I don't agree with other posters who say that this will turn the panel against you but it will bore them because they have heard it so many times before and because it isn't relevant to the appeal. Another no-no is going overboard on the child needing to go to the same school as their pre-school friends - most children make new friends very quickly and easily and if they have psychological problems which mean they can't, the panel would expect to see confirmation by a health professional.
One thing to avoid (if you can) is flinging some crucial document onto the panel's desk just as you start your presentation. They won't have time to read it properly and you probably don't want the delay of an adjournment.
Try to relax, remember that the panel are human (possibly even MNers ) and do the best you can for your child.
MumsVoice - I am puzzled by your post. Everything depends on the oversubscription criteria for the school. I am assuming that the criteria go something like - looked after children, social and medical need, siblings, church affiliation, others ranked by distance. If you weren't attending church and had no letter of support from your vicar, then you would have been considered (I'm assuming again) under the sibling category. Presumably the children who live further away who were allocated places were in a higher priority category. Does your school distinguish between foundation places (linked to church attendance) and open places (not linked)?
I am not sure what a letter from your former priest will achieve. Again, a lot depends on the precise wording of the admissions criterion, but our school requires evidence that the family are churchgoers and have been attending regularly for two years. If you had left your church, then (unless it was a very short break) then I think the problem isn't that you left that part of the form blank, it's that you weren't a churchgoer at the time of application.
How big is the school? Being 6th on the waiting list may give you a good chance of a place before September, if the school is a large one. If you intend to appeal and this is an infant class size appeal (see all the other threads about this) you will need to show that there has been some error or irregularity which has deprived your child of a place.