In Elder Scrolls Oblivion and Fallout 3 I used to collect unique weapons and put them on display in my home. I can't do this in Skyrim because every time I walk into the house I find them in the middle of the floor. Could be Lydia I suppose, jealous of all my collectibles.
You need to drop your items you want displayed on the floor, then go out and save/re-enter the house. Place them where you want in the house now and they'll stay there. If they don't then just grab them and put them back on display, they should stay there this time. But remember: don't put them back in your inventory during this process. Otherwise the house for some reason won't recognize their positioning and just drop them randomly somewhere.
If you do however pick them up, repeat step 1 and try again.
The source for this, you wonder? my own experimenting in Breezehome (ps3) and learning this little trick by myself, heh.