Same issue on the 2011 with the 19" wheels. Take it for an alignment but if yours is like mine an alignment is only going to last a short time. (few months)
Basically the car is tracking any minor imperfection in the pavement. On highways it will track the crown, be in the left lane it pulls left and in the right lane it will pull right. Wet weather exasperates this. I tried Ford and the service manager did not even put the car on the rack before he quoted me an alignment.
I brought my car to a third party wheel and tire shop where they put new tires on and during each rotation checked the tires and alignment. They found my tires when on the front were wearing on the inside corners and cupping, both (according to them) signs of a bad suspension. The alignment was also falling off quickly, they even asked if I was bouncing the car off curbs. They basically recommended a stiffer sport suspension to tighten everything up. They referred to the stock suspension on the Mustang as lightweight garbage.
Suspension they recommend, wheels and tires are going to cost almost $5K. I am just waiting to burn through my current set of tires first since they are already ruined by cupping. Driving around I change lanes to find to path of least resistance and have figured out the really bad areas that I avoid. I also tend to drive more two hands on the wheel as opposed to one handed. Two hands makes the occasional pull, manageable.
Pisses me off that most of the money I have sunk into this car has not been purely performance mods, but to fix Ford's crappy job building a car.
This definitely sounds like the same issue I'm having; have you been able to resolve the issue?