I gave Whiterun NPCs a greatsword each aaand http://minus.com/mJYuSHrQKuGTZ they have it equiped on their hip. When they are fighting, the weapon is still on their hip so they are swinging an invisible greatsword.

lolwhat

I've had that happen with Hulking Draugr as well...

Did you by any chance give them a Nordic Greatsword?

yes. I just wish it happened with Wuuthrad.

I suspected as much. I believe the Nordic Greatsword is bugged for npcs.