The issue I see in some critics here is that it's not a matter of "what could improve the product" but more "what I would have liked the product to be".
If I look at a motorbike and say "well, I think it would be better if it had four wheels, could carry five people and maybe be covered", I don't actually want a motorbike, but an aoutomobile!
Same here. The New Red Box has only the cover and the form factor in common with the Old Red Box.
The ORB was NOT a starter set. It was integral part of the rules. You kept using them from 1 to 36th level. Expert and other sets just expanded the Basic rules.
The closer equivalent to BECMI is Heroes of the Fallen Lands and the DM stuff, whatever is called (don't remember).
The NRB is, instead, a starter set. It's clearly intended as a preview and "trailer" of what is the game. It inherently has little replay value, outside lending it to friends so to get them in the party.
If you already know what a RPG is, you played Vampire or even a computer RPG, then you should probably start with the Essential line, and buying the NRB is a waste of money anyway.
That said, not having it already in hand, I think there are some things that could make it better, without altering the base scope of the NRB.
- A some more short solo adventures after the "guided character builder".
They could start from what the first stopped, using one of the possible created characters, maybe one for the fighter and one for the wizard, which would thus be available as pregenerated characters. Best would be four adventures, one for each of the basic classes, but 2 archetipical classes are better than nothing.
I think this would have been good to introduce some fluff and technical differences to newbies. Skills peculiar to the class. Maybe some more powers.
- A couple more group adventures, possibly in different locales and situations.
Showcasing the thematic differences between dungeon, urban and woodland anventuring, and such the variety of role playing, could be a great asset for drawing new players in, IMHO.