One problem related to engine burning oil has been reported for the 2014 Dodge Ram 1500. The most recently reported issues are listed below.
I noticed that when I started my truck after it had been cold for a while that blue/white smoke would briefly come out of the tailpipe. I noticed it several times and took it to the dealership who said they couldn't find anything. It still did it intermittently. I then noticed that my oil level was low, and the oil pressure sensor went out. I had the oil pressure sensor replaced under warranty and added oil. Based on the excessive oil consumption, smoke, and oil pressure sensor going bad, I think there's something wrong with the engine. All my problems have been oil related!.