This time, though, I saved my game right before I entered Dragonsreach before purchasing the house. I tried numerous different ways of purchasing the house, along with its upgrades and saw some success. Sometimes the weapon racks would work but the upstairs plaques would not. Other times it was the opposite. After numerous trials (and errors) I finally got everything in the house to work properly. My weapon racks, book shelves, and plaques all work, I've never been so happy about such a minor detail. Now, while I cannot say for certain exactly how to go about doing this, it is obvious that it is in some way tied to the series of purchases you make for your home.
I believe, although I'm not for sure that if you buy all of the upgrades prior to going into the house then everything should work. This is precisely what I did. If however you buy one upgrade, say the one with the weapons rack, that one will work but your next purchase will not. In the end, if you are like me and are obsessive over these minute details, I can suggest that you save the game before you make any purchases and keep trying until you get the desired results. It worked for me. With that out of the way, along with the fact that I found out how to move dragon skeletons, I'm finally ready to start "playing" the game.