Ask one of the senior team if they can tell you about staff turnover - how many left last year, how many started this year. Also ask about what percentage of classes are taught by non subject specialists.
Recruitment and turn over are huge problems in schools and much worse in some than others. Don't expect anyone you ask to know the answers off the top of their heads - ask if they can find out and email you the info.
I'd also ask any tour guides how often they seem to have cover or supply teachers, or if they had changes of teacher during the last year.
I'd also ask about how many have the option to do 2 languages or 3 sciences at GCSE and how it is decided who gets that choice.
I'd ask which subjects are set by ability and when and how much movement there is.
If there's a chance you won't get in, speak to the admissions person and ask if you would have got in over each of the last 5 years.
Just be aware that all schools can out on a snazzy evening with science displays and lots of IT running and practical stuff going on all over the school, plus glossy displays.
Ask roughly what % of intake are high, medium and low achievers - and consider how this fits with your own child.
Lots of these QS might need need someone to get back to you - leave your email address and do t worry about being the slightly annoying person who asks the rather difficult questions.