I've worked in a secondary school that was "inadequate"- however, it was just inadequate in one area, and assessed as good in the areas that related to teaching and learning and the school experience for most students. Our exam results were generally good. We were taken over by a MAT, and at least initially there was a very rocky period for the school- it was not rapid improvement, and I would say there were times when things got worse.
It's obviously not the be all and end all, but if you can find out last year's GCSE results and progress 8, that could give you some indication as to whether the school is improving.
Even if there hasn't been another full inspection, there should also be interim inspection reports available for a school like this.
Things I would be concerned about and what to find out more about:
Does the school struggle to recruit teachers, particularly for core subjects?
What is behaviour like in lessons? Is there lots of low level disruption?
What is the behaviour policy like? Is it actually followed?
What options are available at GCSE?
What are the destinations for students at post-16 like?
What is the extra-curricular offering like?
Ideally, I'd want to have a look around during the school day. However, this is unlikely to be possible.
Are there really no other schools available that you could apply to? If they're under subscribed, it won't matter if you're not in catchment etc?
On mumsnet, you will get a lot of people who tell you a bright child will do well anywhere. But even a bright child will struggle if they don't have stable teachers, and every lesson is being disrupted by other students. I also think a lot of teens do change to fit in with the environment- if aspiration is low, it will have an impact.
There are really bad schools out there, and some I would not want my child in. Is moving house an option?