i'm suprised the dealer covered the repairs.
not trying to be an ass, but its common sense that any vehicle with 4wd/awd needs to have same size(diameter) tires front to rear. you literally overheated and destroyed the transfer case on your car. awd systems usually allow for some slippage, but different size tires is too much.
those tires you put on were 3.33% different that the others.
use this site to calculate tire sizes.
http://www.1010tires.com/tiresizecalculator.asp

 

+1

If you want a cool set of wheels that normally come in staggered sets, just buy 4 fronts (assuming the offsets are ok).

 

Just to clarify, it's not the staggered setup per se that's the issue, it's the somewhat different rolling diameters. Maybe it's within tolerance mathematically, but I'd think there'd be some warranty concerns even if it were very very close. Audi I believe, except on the R8, runs identical wheels all around on their quattro systems for just this reason. This is all just my opinion - raises alarm bell though.

 

I have a 2006 530xi. The post above is right. You probably fried the transfer case. You cannot use different size tires on the car (*except* in a very limited case - more below). The problem is that there is a differential between the front tires and the rear tires - the transfer case. The transfer case is built to run the front and back tires at a specified ratio. In the case of this car, the front and rear roll at the same rate. I looked in the Owners Manual and pasted in the tire page for the xi cars. If you notice there are two set ups that have front and rear different. But, if you calculate the characteristics of the front and rear tires, they have nearly identical revolutions per mile. You can find one of these tire calculators here: http://www.tiresizecalculator.info/

 

BMW covered the damage under the CPO, I thought I was lucky. My advisor actually said you need 2 new tires ASAP or else you will be back here again and we will not cover the damage then. I've owned my car for a few years now but did not know much information about the AWD system. When I went to purchase 2 new tires no one would sell me just 2 tires. They said if it is an AWD car you have to buy 4 because ALL tread patterns, tread wear, tire size, and tire brand has to be identical. Because if they are different you can damage your AWD system. This is all new to me.