Since the car is still very new, nothing has gone wrong.
The transmission, although likely OK, sometimes shifts roughly.
Although too new to tell, I have heard from a few other Galant owners that the brake system has some problems; they have had to replace the pads and/or rotors every 5-10,000 miles.
This car handles very well and has a lot of power for a 4-cylinder automobile.
I got the car with the premium leather package and the seats are amazingly comfortable.
The 7-speaker Infinity sound system is one of the best I have heard.
For the $22,000 I paid for the car, it is completely equipped with power everything (locks, windows, 10-way driver's seat, moonroof) With all of the power features the leather seats, steering wheel and shifter, Anti-lock braking system standard, alloy wheels, cruise control, etc., you can't beat the price.
My only complaint is that the interior finishing is a little boring. A lot of comparably priced newer cars have chrome accents inside or burlwood trim. The new Galants are finished with bronze or titanium accents which look cheap; the titanium trim doesn't stand out well against the tan interior of the car.