Lion, since you mentioned Checkhov's gun, was there ever any narrative purpose of Skylar's affair, Walter Jr.'s disability, or Marie's kleptomania?
I don't think Skylar's affair would pertain to Chekhov's Gun, since it was a
result of previous plot points, not a pre-existing plot point of its own.
I think Walt Jr's disability was used as a vehicle to illustrate a preexisting hardship for the family, which progresses the idea and makes Walt "breaking bad" a greater extreme. This might be illustrated in the scene from season one, when the jocks at the store are making fun of Walt Jr when he's looking at jeans with Skylar... Walt comes in guns blazing, which derived from Walter Jr's situation.
Marie's kleptomania is a vehicle to make you sympathetic to Skylar, IMO. It's natural to have mixed feelings about the Walt/Skylar relationship; even though Walt is being shady, Skylar could at least work with him a bit, and not turn the cold shoulder so quickly... what you can't really question, though, is Marie being in the wrong when it comes to her plot with Skylar (the tiara incident). They show Marie as a klepto, and then use that to give something for Skylar to be clearly and rightfully upset about. It's a hard line that the audience can use to sympathize (just a bit, and early on) with Skylar, while the line between her and Walt is so blurry.