The vehicle stability system had problems with the mismatched tires because each of the wheel sensors were sending different speeds, which would be telling the computer that the car was out of control. But the mismatched tires would not cause any mechanical damage as long as the tires on each axle were the same. Even a side to side mismatch in the rear would not cause any mechanical damage.
A side to side mismatch in the front would cause the vehicle to pull to one side. It would cause the spider gears in the differential to always be spinning too but as it is not a limited slip differential, that wont hurt anything either. I suspect your groan is not related to the tires.