One problem related to transmission not go into gear has been reported for the 2013 Ford Mustang. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2013 Ford Mustang based on all problems reported for the 2013 Mustang.
I was unable to shift gears while driving and the service dept advised I had bad synchros and was fixed under warranty. Fast forward a couple of months and had difficulty switching gears from 1st to 2nd had really bad grinding and would take a couple of times to shift. Then, when starting my car from my house, I was unable to get the gear into reverse while the car was on. It just wouldn't go in to gear. . . Not any gear in fact. I had to turn the car off and put it into reverse and then turn the car on. While the clutch was fully pressed down the car started moving backwards when I removed my foot from the break. (the car was level and that never happens). Then after backing up I couldn't get it out of reverse. I had to turn the car off and put it in 1st and then start the car. The same thing - it moved with the clutch in and couldn't get it out of gear. I had the car towed to the dealer's service department. After the tow, for whatever reason, they were able to drive the car without issue. I'm not used to driving a car with such transmission problems that can't be diagnosed.