Continuity mistake: Walt comes over to Jesse's house to tell him about Hank investigating Gale's murder. Jesse is shaving some guy's head. In one shot, the guy getting shaved has less hair. More hair instantly appears seconds later. (00:26:20)
Continuity mistake: After Walt and Junior are about to go see Hank's mineral collection, Hank's front door is still open. The camera cuts to Hank for a moment as he turns his wheelchair to move down the hall and Walt and Junior soon follow. In the next shot, suddenly the front door has closed by itself. There was not enough time for Walt to have closed it and it would have been heard if he did.
Chosen answer: I'm not sure how far you are into the show but he does eventually come up with a way to launder it (wont spoil it for you but rest assured, when he gets a lawyer the show gets much better!) and in the final season he also comes up with a way to give his children his money without the cops or the DA knowing it came from him.
The_Iceman