These cars are new, so we haven't worked on one. Some problems are due to people driving the DCT like a normal automatic transmission. It is closer to a manual transmission that it shifted automatically. The trans computer looks for things like throttle input and vehicle speed to determine what gear is the best one to be in. For the sake of fuel economy, the transmission will try to put the car in the tallest possible gear at the time. This can lead to some groaning from the engine- like a manual in 2nd gear at <5 mph. This sound is most likely the "grinding" that some DCT owners complain to Ford about, and Ford can't find a fix because it doesn't act like that when the service techs take it out for a drive (see Ferris Beuller's Day Off).
The way I see it, there are 2 possible fixes you can try from your end. 1) Use select shift. In this mode, the transmission will not shift into the next gear until the engine is at its maximum rpm 6800-7000, unless you tell it to by pressing the "up" button. Use the select shift until you're moving, and then knock it up into D when you feel like you want the computer to take over. You can read about select shift mode in your owner's manual. 2) Reset the modules/ drive differently. Ford computers (all OBD2, really), learn from driver input, so you might want to clear out all the information from the previous owner and test drivers. This might really cause some stress because of all the MFT settings you might have, but hey, at some point in the car's life you're going to have to do this anyway. You might as well learn now while you're in control. Disconnect the negative battery terminal for about 10 mins. Replace the terminal, tighten, and start the engine. Allow the engine to idle for a minimum of 5 minutes after the rpms have fallen from "cold start" mode. Do not be critical of engine rpm during this time. If the new Focis are anything like the old ones (and I think it's logical that this operates in the same way), a reset ECU will perform tests to determine the optimum air/fuel ratio. During this time the idle will fluctuate slightly, and be slightly high. When the test is finished, the idle will drop to where it should be normally- around 700 rpm. Now this time when you drive the car, be careful to avoid the "why doesn't this act like a hydraulic automatic" trap. Try to keep your foot on the brake pedal until it's time to move the car- just like it was a manual transmission. Don't hover or allow the car to creep forward in gear. Either be on the brake or on the gas in a low speed situation. Just like with a manual, the effect of being in a tall gear isn't that big of a deal once you're moving.
You can find a lot of text written on this site about 2012 Ford automatic transmission problems. You'll probably find people who were in the same situation as you're in who never resolved it. You'll also find a lot of people who tried advice like this, and that solved the problem. We've had more than one Ford mechanic report back that people who trade their car in for "transmission" problems don't have transmission problems. Then there are people with real transmission problems, who IMO, get shuffled around like they don't have problems because there are so many people without problems who swear up and down that they have problems. The real transmission problems are : car not moving while in gear, burning smell while driving, loud humming at highway speeds, and car stalling at every stoplight if not shifted into N. We don't get many of those, but it is sad that when one does surface- the person is more likely to be ignored by the dealer than have the problem repaired on the first visit in. For situations like that, we have a Ford Customer Service representative on this site who can help make dealers cooperate if they are being uncooperative. In your case, I hope you'll try my advice and not think I'm insulting your driving skills. I also hope it works out for you.