How are tutor groups arranged? In random groupings? Streamed? Vertical tutor groups ( mixed ages in a tutor group - for registration etc, not for teaching). Do they keep the same tutor throughout their school career?
Setting? For which subjects? When? i.e when do they put them in sets? How many ability levels in the sets? How much movement between sets/
If streamed - when? How mobile? Do they set across streams? (i.e can someone in a middle set who is a whizz at languages study in top steam language classes)
How many MFL can they study?
Can they do more than one humanity at GCSE? (many schools seem to be able to offer each student either history or geography)?
Can they do triple science?
What languages can they study? Mandarin / Japanese / Latin - whatever you might be interested in.
Anything of specific interest to your child; what sports do they do and what sports do they have a school team in? What are the arrangements for music lessons - can they arrange music lessons in school? What music opportunities are there? School orchestra? Choir? What drama? Do they do a school play that they can take part in each year?
What is the extra curricular - after school programme?
What is the arts offer? Do they go and see proper theatre or to proper galleries? Have artists and writers in to school? Do they have Artsmark?Artsmark Gold?
How do they support and challenge children of high ability in any given subject? How do they enable children who need support in any given subject? (as likely to be applicable to your child).
What qualifications do they offer in addition to GCSE - BTec? Can non-academic kids get good qualifications?
Consider how long the Head has been there: are they new and pushing up standards (but it takes a little while), or have they been there ages and things are going downhill a bit? Or experienced and flourishing...and might retire soon?
Is the school taking up new opportunities, making new partnerships?
In terms of the published results - look much closer at the figures available on the Dept of Edn website. The raw stats - how many kids get A-C GCSE doesn't tell you anywhere near everything. How many children in each ability band make expected progress? Which band of attainers seem to do best against targets? Are the results a reflection of the intake, or of the teaching? (you can tell this from the ratios of high , middle and low attainers a school, has in it's intake). In a school with very low overall results, do they have a high % of low attainers in the cohort and a small number of high attainers doing fantastically well? Are all meeting expected targets?