I don't want to be overly critical of Drew because he's a pretty good QB (especially in regards to taking care of the football). He seems to take quite a while to go through the progression of his reads (and he has a bad habit of "patting" the ball while he does it and has happy feet as well). He throws it much better when he's just completely committed to a throw if he gets the coverage he's looking for like on the TD pass at end of 1st half.
On plays where he has to go through his reads, he takes forever and almost always throws the ball late to the receiver he ends up choosing allowing defenders to close on the intended receiver. He's got to make his reads and final decision quicker.... and get the ball in the air. Honestly, most great QBs have said that if they can't find someone after a 3 or 4 count in their head, they take off from the pocket causing defenders to adjust to the fact the QB is in open space... then they either run for as much as they can before going OB OR throw it to an open receiver on a broken play "come back to QB" route. If you watched the Steelers game last Sunday - Aaron Rogers did this over and over (granted, AR has one of the most accurate arms and quickest releases on the move ever).