American police kill about 1,000 people per year. There's a thing going round saying that US police in March killed more people than UK police killed since 1900 but none of the sources look particularly reliable.
Several bad shootings over decades? What's your point? What a strange thing to say.
We don't shoot many people, America do. It's such a huge, cavernous gulf in magnitude that I have no idea what point you're trying to make with your last paragraph.
I'm saying that it's wrong to think that armed police officers do better than armed US officers. We mostly don't have armed officers over here. Where they are armed mistakes happen and people die, so it's important to keep UK officers unarmed.
Also: yes, even those few deaths are totally unacceptable in the UK. People are shocked by police shootings; investigations are rigorous. Contrast that to the US where shootin a dog sparks mass outrage but shooting a drunk pregnant woman doesn't.
About half the people killed by police have mental health problems. This is an estimate because national data isn't collected. http://www.theguardian.com/us-news/2015/apr/03/idaho-police-...
http://tacreports.org/storage/documents/2013-justifiable-hom...
But, for the UK, don't forget the several bad shootings of innocent or unarmed men. Wikipedia has a list of all killings involving a police officer in the UK. http://en.wikipedia.org/wiki/List_of_killings_by_law_enforce...