In reply to woolsack: Or you could ignore stupid 'rules' made up by cliquey idiots and consider safety on the road. That said...
I've never seen the point of helmet mounted mirrors - they seem to depend too much on head position to work reliably.
I tried the Mirrycle brifter-mounted rear view mirror and it was rubbish. Maybe OK on billiard-table smooth roads but it vibrated all over the place and was always slipping out of position on the appalling surfaces I encounter round my way. (Note to Edinburgh council: just because the tarmac isn't actually falling apart doesn't mean that the road is actually servicable. If the top layer of metalling has worn in to patches it feels just as bad on a bike as the cobbled streets in the city centre.)
You can get mirrors that mount on the down tube. I've never tried one but it looks to me as if the rear view from there wouldn't be great.
I've also seen mirrors that fit on the end of the handlebar drop. I suspect that they would be as vibration-prone as the Mirrycle turned out to be.
So as it happens I am rather skeptical about mirrors on bikes, but not because some self-appointed 'style police' forbid them.