Main thing when you do mix tyres is 'never' mix an asymmetrical tyre with a symmetrical tyre, this is when BMWs throw a real wobbly, more so than mixing say a Michelin Pilot Sport ZP with a Michelin Pilot Sport 2, which have the same tread just different compounds.
The worse case I have experienced is with a Michelin Pilot Sport 2 on the rear and a Michelin Pilot Sport 1 on the front, I thought the car was knackered, 3 techs also through the car was knackered, they replaced front wishbones, rear trailing arm bushes, top mounts and rear suspension and still no better.
Then somone who races CSLs took it out, we pulled off the roundabout and took the first corner and he looked at me and said "You've got mixed tyres on this!!"
To which I replied "Nope, they're all Michelin Pilot Sports."
We got out and that was the first time I had clicked that the fronts were 1's and the rears 2's. Put 2s on the front and everything was perfect again.
I think as the car gets more powerful it starts to show how bad mixing tyres can be, I spent a week with run flats on the front of my 320d touring and Michelin Pilot Sport 2s on the rear and that was not bad unless I pushed it in the wet, but generally not enough grunt to make the back snap out, but still noticed that it was not 100% planted sat at motorway speeds. The CSL put the back end out overtaking on the motorway at 60mph, that is how much it affected that car.
I just don't see why anyone would buy a BMW and then put mixed tyres on it?? It turns a great car into something a bit shit.