Why did Shaker have Mullen change clothes at the gym?
I understand that he made him retrieve the locker key from the bottom of the swimming pool because he knew Mullen might be wearing a wire(which he was) and that he had him get in a new car that wouldn't have a car phone so Mullen couldn't call the apartment and tell the feds where he was going--same reason he told him to leave the phone in the locker behind--and he had him transfer the money into a new pair of bags because he knew the suitcases would be equipped with tracking devices.
But why did he tell Mullen to put on the cap and overalls? Was it out of the kindness of his heart because he knew the guy was wearing wet clothes?
Doesn't sound like Shaker to me.