I can see two problems that are missing here for real Dzeko to come.
Lack of team play - Said enough in recent posts
Dzeko is still soft on the ball, lacks confidence and arrogance.(Also deal with Boateng). Defenders push him with arms, elbows and what else not but he does nothing. German league prevent this but EPL does not. He must use his hands and arrogance when getting the space, instead he only uses his body. Thats why he has a bad time when receiving a pass, because in the start there are 1 or 2 players coming from his back, pulling him over. This is also the deal with long balls, because it is evident that defenders push him with elbows or just rely on his back (Germany - foul) so he cant get the ball right. He knows to give a good pass and has the intelligence but as a forward he must feel a ball a little bit more. He almost always bass the ball after 1-2 touches and runs to the goal, but you dont see other players doing that as they always have 4-5 touches before making a pass. There he lacks confidence, because I only seen him 3 times going to the area with the ball in these 4 games( everytime got a freekick). At Wolsfburg, he had 5+ crosses like that in one game. He is in the different team, different players and the system. Only thing he needs is to have a ball more often, keep it, try to get past the defender and thats the only thing he needs. Lose it what the heck, Tevez lose it 10 times but then scores a goal.No point of pass the ball on the first touch when you will not get the same service from teammates. If he does not have touches with the ball more often , I afraid that it will cause him going deep into himself, causing barriers in his mind. And thats it. It is not the skill, not the pace, it is only in the head. The same thing is with Boateng.