Much like the Nazi had one.

On paper it's neat and clean, in practice it's as big a mess as the Light was not so long ago (and in some ways, still is), with the DO giving redundant or divergent orders to several of his Chosen, agents scattered everywhere, everyone pushing and pulling in any given direction, Forsaken having spies on the agents of the others and trying to interfere with plans. At the DF level, they obey their orders when they see no other choice, otherwise they're very keen to do whatever will serve their own interests (eg: Daved Hanlon/Mellar).

In Caemlyn, you had Shiaine answering directly to Moridin, Mellar answering to Shiaine and Moghedien, several BA who long ago failed to find Moghedien and gathered in the city, pursuing their own goals and ending up coming to see what the heck was going on with the sisters at Shiaine's. Etc. It's very typical of the way Moridin manages things.

In the middle of this, Moridin rarely lift a finger (until WH or so). He lets his DF circles be scattered all over the place (Shiaine was based in Caemlyn and ended up for a while in Ebou Dar out of reach of the circle she lead... Same for Paitr we saw near Caemlyn in EOTW and later in Amadicia) and used as the other Chosen see fit - something receiving competing orders from more than one, he didn't lift a finger to force the others to let the BA to Mesaana for e.g., and so on and so on. He let that go on for a long time. Plans failed, plans clashed with one another, it didn't seem to matter to Moridin in that phase as long as it created chaos. It's only now the endgame is approaching that Moridin brought some focus among the Shadow's forces. He's reached the point where some specific goals need to be achieved, and he needs to have some order and focus for that.

I don't think "organized" is really a good adjective to qualify the Shadow.