Nope, skyrim and half life 2 both use the havok engine.
Ah, indeed. Thank you, sir.
If you use weapon racks, mannequins, etc (with an inventory menu), you shouldn't have any issues because the items displayed on those won't have any physics properties. As soon you just (litterally) drop them somewhere in the house, these bugs can occur.
I think the introduction of weapon racks, bookshelves and mannequins are Bethesda's solution to this problem. You can still display all your pretty stuff without fooling around for an hour to get that two handed sword in the right angle...