On a recent trip to New Jersey, I had the misfortune of having my right rear tire go flat with damage to the sidewall. In a rush I ended up getting a ContiSportContact installed, while leaving my stock ContiTouring on the three other wheels (essentially no tread wear, car only has ~6000 miles.)

The car seems to be driving fine, but are there any problems that my arise?

 

As long as the two rear tires are the same size (OEM 255/35R19), no problems from a mechanical standpoint. And I won't tell.

 

look at it this way, at some point if you decide to switch tire brands, you'ld end up with unmatched brands for the front and rears as I would think your 4 tires are not wearing evenly (ie. rear tires wear out faster). I've had un-matching rears and fronts with very aggressive driving with no issues as i've tried different brands since 2005. Can't speak for driving in snow though as my car has never seen snow.

 

Hopefully they are both the same bias - radial OR crossply - DO NOT MIX.