It won't matter what he does. He can bust his butt, all offseason, do everything right, and he can lead the Cowboys to an 8-0 start for the season and the moment they lost that ninth game and dropped to 8-1 he'd be blasted for not caring enough, for sucking, for being the biggest reason the Cowboys lose.
Heck the guy could (and I'm certainly not saying this will happen or anything) Dallas to a 12-4 record, 3-1 down the stretch, win a playoff game, or two, and the moment they lost a playoff game, or the Superbowl, people would immediately bring out their pitch forks again and say, "Oh well Tony chokes everytime. He can't win big games. He can't do this. He can't do that."
I hope he's able to continue to improve, and continue to help Dallas improve, but it will never be enough for some.
That said he certainly has things he needs to improve in individually. Learning to throw the ball away, learning to tuck that ball in tighter when he's having to scramble around so that it doesn't get stripped when someone comes from behind to slam him to the ground. Learning to take off and get the little 5-8 yards on the run, that are there, instead of waiting, and waiting, and waiting to try and make the big play and either throwing that dreadful pick so many complain about or taking that hit from behind that causes a fumble.
Plenty of room for him to grow, and learn, and get better. I personally believe he will. Time will tell I suppose.