I am going to sign in right here: "on vision cone"
If a player's head is moving around too much and the QB looks at the field too much, this is seen as a weakness by some coaches. ( and players )
The reason being is that the player may have under-developed mental mapping skills, not enough practice, new plays, etc. A well developed QB's head does not always move. He has command of the play and the defense, so he uses his head to direct the play, for example looking off 'looking off coverage' and hitting empty space for YAC passes.
Montana, Fouts, Namath, Warner all talked about this skill at some point. ( I think Manning has too, but I don't remember )
This doesn't mean every quarterback is the same, it just means you have one more thing to think about when you are are looking at Dave play QB.
IF his head 'isn't' moving, it does 'not' mean he is 'not' seeing the entire play. A finely tuned QB in a play working out exactly the way he planned, does not need to look with his eyes to see what is going on. He already knows.
IF his head is moving, it can mean that there are problems in a play. Something didn't happen the way it was planned, so he has to start to look and see what is going on. This can be caused by a myriad of things and not just the QB; line breaking down, wrong routes, slow routes, game planning and preparation failed, etc.
here's a clip from NFL.com
"It's mind boggling right now," said McNair, who signed a five-year contract. "I think the verbiage is the most important thing right now. Once I can feel comfortable and visualize the formation and the routes that they're running, things will be OK." But, he added, "It's like starting all over again."
Here Steve is talking about "visualize" the formation and routes. This does not mean looking at the routes. This means he knows where everyone is at, at any given time so that he doesn't "have" to look.
A three-time Pro Bowl selection, McNair often appeared hesitant. He completed his first pass in team drills to tight end Todd Heap, but struggled at hitting receivers in stride. One late, errant pass was nearly intercepted, but defensive back Robb Butler dropped the football.
Inability to visualize or create the mental map, makes hitting open space for YAC passes that much harder.
"A confused quarterback is usually confronted with a barrage of blitzes. If he's confused about protections, that's when he's going to get whacked," Fassel said.
So if a DC sees Dave's head moving around too much, he might be inclined to let slip the zone-dog-blitz and cry "sack him".