As I consider your examples, I find that there are things that I think of as "normal living room clutter", and therefore the job of the person who tidies the living room, and other things that I consider to be the job of the specific person who caused the clutter.
As I see it, normal living room clutter is what occurs when people use their living room in a reasonably relaxed fashion, without worrying about hopping up and putting things away the instant they're done with them. I consider the cleanup to be a worthwhile price to pay for the relaxation. However, that means that it's a problem for the _same_ person to always do the cleanup, because they're the one who's always paying the price, while everyone else is benefiting.
So I think that your DH should sometimes be responsible for tidying the living room, so that he can understand the annoying elements, and so that _you_ can occasionally enjoy the relaxation of hanging out in your living room without knowing that you'll have to tidy the clutter.
I don't know what that "sometimes" would be, but it seems logical for him to have the job on weekends and all other days off, like holidays and at-home vacations. This is on the assumption that since you usually take care of the kids, you have more work to do on these days off than he does, because it's hard to swap some tasks on a day to day basis.
And if older DS is old enough, you could also assign him the tidying job on some days.
So, that long long ramble was partly to introduce the idea of "normal clutter" and "clutterer's job". I'd say that, going through your examples:
- Hangers: Clutterer's job. Adults--and children beyond a certain age, for that matter--should put the hanger from a garment back in the closet promptly, as a matter of course. If he doesn't want to walk back to the bedroom, he can just remove the garments from the hangers when he gets the garments, rather than carrying them into the living room, hanger and all.
By the way, why is he dressing in the living room? Is there something about the bedroom that makes it inconvenient to dress there, and is it possible to fix that to break this habit?
- Shoes: Normal clutter. Is there a designated place in the living room to kick off shoes? We have a bench that we kick them under, and every few days when the space fills up, I carry any excess off to the bedroom. While perhaps people _should_ walk to the bedroom, take off their shoes, and come back, I think that coming-home habits are the hardest ones to break, and that it would therefore be worthwhile to designate a place for shoes in the living room. If he doesn't change his shoes a lot, maybe his everyday shoes could just live there permanently.
- Packaging: Clutterer's job. Similar to hangers; the person who gets the package should deal with throwing away the associated trash, and should do so promptly. Is it pretty easy to throw the trash away? If it's difficult - for example, if you have to go all the way to the cold garage and squeeze past the car to put the box into the recycling--then it might be worthwhile to make it easier for all of you. But in general, yeah, the package recipient should be dealing with this.
- Remotes: Unsure. A few remotes is, to me, normal clutter. A big tangle of joysticks and cables and little control boxes is "clutterer's job".
- Newspapers: Normal clutter, unless they're all pulled apart and covering a whole lot of square feet.
- Gym bag: I'm undecided, but leaning toward "clutterer's job", and again wondering about how to break his habit of dressing and dealing with clothes in the living room.