This intrigued me because no other house I had ever bought had come with working containers, so I saved my game and tried to remove an item from my inventory and place it in a box. Well, the item was removed from my inventory, but it didn't appear in the box's inventory. In fact, no item I put in the box seemed to appear in there. Rather, the box just seemed to be eating all of my items.
So I loaded a save file I had made in the house just minutes before and I got all my items back. But then when I tried to click on the containers, they didn't work any more (as in, no inventory screen opened or anything). So I left the house, and when I came back in I could open the containers again - but they still ate any items I put in them.
Anyway, following this experience I decided to dig around on the UESP to see if this is a common bug, but I wasn't able to find any information about it. So now I'm going to ask the Daggerfall veterans on the Bethesda forums here: what's the deal with these house containers?