Wizard, what any previous edition had that denoted a given monster race's world-place and interaction that isn't present in the 4e version.
I'm not Wizard, but what I've found from my read-through of the 4E MM alongside the 3.0 MM is the 3.0 MM has a lot of wasted space with a few absolute gems that the 4E MM is lacking. Aboleths "know many ancient and terrible secrets, for they inherit their parents' knowledge at birth and assimilate the memories of all they consume", the young "remain with their parent for some ten years, obeying the older creature utterly" and "[hope] their prey will enter the water, which they ften make appear cool, clear and refreshing with their powers of illusion". Azers "maintain a tightly regimented society in which every member has a specific place". "When not hunting, basilisks are usually sleeping off their meal", "a basilisk's lair is sometimes distinguished by lifelike stone statues". These are tiny, flavourful snippets that could be included in the 4E MM, but weren't. I think that was a huge mistake.
For what I consider an excellent 4E entry, take a look at the cyclopses. They have this great backstory, an excellent connection to their masters, the formorians, and an out-of-combat role as master craftspeople.
I think if I were writing a 4E MM, I would insist that the entries include:
a) What the monster does, when it's not fighting.
b) How to detect the creature when it's not at home (e.g. piles of brains, which chuul don't eat)
c) Replace the encounter groups prose with details on HOW they interact with other creatures, not just a list of the creatures they interact with.
That said, the 4E MM is still my favourite MM - in fact, it's also my favourite 4E book.