
Continuity mistake: When Walt walks into the house at the start we can see the kitchen has a window and it's bright sunshine coming through. However, a few minutes later we see the kitchen behind Walt and it's in complete darkness despite the previously mentioned window. (00:04:50)

Continuity mistake: When Walt breaks the news that Gray Matter is broke, Skyler's hands are on her stomach, we then see her hands are by her mouth. (00:38:50)
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