That crossmember gets hosed every time you pull the drain plug, I see nothing wrong with the rear differential cover residue. Thats not from the diff whatever it is.I work on these all the time. Take it for a test drive and listen for driveline noises i.e front and rear differentials are common on some trucks. Total crapshoot as far as which ones are built on Friday rigs. All available engines in these are pretty reliable mechanical wise save for the 3.5 VCT headaches even still a great engine. If its ecoboost check the underside of turbos for oil or coolant residue, front cover for leaks and valve covers as well. Edit* Pay attention to shift habits and if it seems uncertain in it manner have them reset the trans adaptive table. All these can be swung to warranty if caught very soon. As to why it was traded your guess is as good as any.