He had the ability to audible but from what it looks like now he has the ability to call his own plays or if he sees an edge against the defense he can call his own play. Just listening to The Fan over the last few days its seems he didn't have nearly the freedom I think we thought he had.
I don't think it's quite call his own play, just more flexibility within a play. Under Garrett/Moore, he could audible out of a pass or into a pass, could change the direction a play was run, etc. He might have two or three plays total he could switch to. Under McCarthy, it sounds like he's going to be able to actually alter routes within the play. If he sees the defense playing back, maybe he motions to a receiver to run a slant instead of into the deep middle, nothing else changes by that. It's not that huge of a change because the receivers had options for their routes based on the coverage, but this way Dak and the receiver both know exactly what the receiver is going to do. The disadvantage of it is that the defense is going to try to disguise coverage so that Dak sees one thing and adjusts the route while the defense actually is doing something else. Since the receiver can't sight adjust after the ball is snapped, he just has to essentially serve as a decoy. Of course, maybe that's why we are working on more check-downs to the backs. If Dak reads it wrong, he can dump off and move on to the next play.