It is actually quite hard to give completely reassuring answers because teachers vary, children vary etc. I can say that a few years back the school had real problems recruiting and retaining staff, but I don't think that's a particular problem any more.
My two kids are very different - dd1 is quiet, well behaved and doing very well academically. She has a tight circle of friends and they are all heading for good RG unis or Oxbridge. She has not been tutored. I am a working single parent and have very little time to get involved with her education. Teddington served her well.
Dd2 has special needs and has always struggled with school - she doesn't go very often. When she does go she is very far behind her peers. Now I won't go into the many ways she has been let down by the system - mainly by CAMHS. But I will say that her teachers are on the whole very kind to her and I am grateful for their support. Teddington has been good to both my girls.
There are some kids with behaviour problems at the school, of course there are. (Most of them are friends with dd2, sadly.) A few years ago the school was struggling to manage low level disruption, but this has greatly improved. The school also works hard to keep on top of any antisocial behaviour after school, at the bus stop etc. Both my kids feel safe at school. Dd1, who is very introverted and a lover not a fighter, never had problems with bullying.
I do think it's important to emphasise that Richmond is a very middle class Borough with a lot of good schools, none of which face the challenges of some London schools. It's easy to get caught up in percentage differences in GCSEs between the neighbouring schools, but a small number of pupils can make quite an impact on one years stats. It doesn't tell you much about added value, and a high proportion of these kids will do well whichever school they go to.