I'll relate this again. This is based on my own personal experience. 1) My 348 felt fine on the road, but the rear tires were worn out. They had a totally normal wear pattern. The front tires had less than 50% tread wear. 2) I went to Costco and purchased two new rear tires, same brand (Bridgestone), same speed rating, same size, same tread pattern, and had them installed. 3) My car instantly became undriveable at freeway speed. It wandered BADLY. It was difficult to hold the car in one lane at some times. I rechecked the direction of rotation, the lug bolt torque, the tire pressures - everything was fine. 4) I returned the two new rear tires to Costco, and purchased four new tires (also Bridgestones) from Tire Rack, and had them mounted and balanced. 5) Once again, the car felt perfectly normal on the road, at all speeds observed (I don't claim to have driven the car over 110mph). There was no break-in period needed. What I DO know: With no other changes, the car immediately went from perfectly fine to totally awful after installing the two new rear tires. What I DO NOT know: What was wrong with the car after I purchased the two tires from Costco? Was something actually wrong with those tires, or was the problem that I only installed new tires on the rear? In my own case, the problem was NOT due to alignment, or faulty shocks, or faulty bushings, or any other mechanical issue. It WAS the tires. But I can't identify the specific problem with them.
Same experience as Miltonian. I expected it to feel a little loose at first; however, it was much worse than expected. Anyway, I kept it at safe speeds and went on several 200 mile trips. I don't know if the tires needed some rubber scrubbed off, or if they needed to go through a few heat cycles, but the car handles great now. I think if you replace all four tires at the same time, it won't be as noticeable since both front and rear tires will have the same handling characteristics at the same time.