In chapter 11 of Deathly Hallows, Lupin claims: "It’s impossible to track anyone who Apparates, unless you grab hold of them as they disappear!". I'm not sure if this true. I was certain that one of the premises behind the plot to move Harry at the start of the book was that The Department of Magical Transportation had been taken over, and therefore Apparation could be tracked. What have I misunderstood?
I suspect that some quotes showing what taking over the department actually meant will be helpful in forming an answer.