Also, I am level 71 on Skyrim, and have not had these problems with houses in Whiterun or Markarth... Solitude DID have 2 weapon racks bugged though.. So I know it's not just me being unable to figure out how to use it.
I bought the Windhelm house after having completed the cival war quests, being on the Imperials side. I'm also thane if that matters.
I did both parts of "blood on the ice" quest with no problems as well.
Spoiler
I got the court wizard in jail, killed the real criminal (Crixtaco or whatever), Had no bugs in any part of the quest.
The problem i'm running into though, is the Weapon racks, Weapon Plaques, and Display Cases.
I bought and reloaded 4 times, hoping they would work, but to no avail.
I then bought ALL upgrades at the same time, as I heard this may fix it, but this also did not work.
The 3 Mannequins and the bookshelf in the armory work.
Everything else in the armory does NOT work, it doesn't even give the option nor SHOW text such as "Activate weapon rack"
Heck.. It doesn't even read the Weapon Racks and Weapon Plaques as actually being there when I attack them with a sword. No sound of hitting anything... no wood or anything flying in the air.
I have tried with no weapon equipped, a dagger equipped, a 2 handed axe equipped, one handed sword equipped, heck.. even the Plaques and such don't show "Activate" OR WORK.
Same for the Displays, except for the ones in the bedroom.
The Weapon Plaques in the enchanting room are also bugged.
On the bright side, All bookshelves in the entire house work perfectly... But sadly I don't know if I should even continue after having bought the stuff if I have to do something to fix the Weapon racks and such before buying them.
I'd just have to load my save before buying the stuff, which is fine, but I don't want to get more artifacts and such and find out I have to load the old save.
So please, if ANYONE here knows ANYTHING about how I can have working Weapon Plaques and such on my 360 version, Please tell me.