Not sure if this has already been posted or not but I have built every house in the Hearthfire DLC and NONE of the display cases work. Is there a patch in development to address this issue?

What do you mean they don't work?
They should work the same way they do in oblivion

Display cases should open then you have to put objects in them by going into your inventory, dropping the object on the floor then press and hold A over the object to grab it. After grabbing it you move it over the open display case then drop it in.

Ive tried this method but objects that i put in the case keep popping out of after i place them there-

Well that problem has been in the game since it was released, the item is usually just where you dumped it in the first place, the game has not recognised that you moved it. Dump your potential case inhabitants or decorating items straight on the floor. Rush down to the basemant if you have one, or just out the front door. Come back the silly house should recognise your items and let you arrange them as you please.

There are still several unique problems to foil you though, most if not all the helmets that refuse to display on the mannequins, will also refuse to be arranged, you want them somewhere you have to drop them exactly where you want them to stay. Some weapons will fall through the case, even though you took the right precautions to ensure the weapon would stay put. These rare weapons could henceforth refuse to display properly on weapon racks and plaques. If the weapon merely decided it was going to half stick out of the case on your return, it will also be ruined for being automatically added to the old display cases as well, it will always display half out of the case. These same bugs go for ALL the display cases, so anything you could previously put in will be fine. It is often the special enchanted weapons you got when you became thane that are the main culprits. Saving your game before you arrange the objects in your display cases (or even before you dump them all on the floor), and then keeping that save till you arrange everything, return and are sure everything went OK can avoid the problem.

If a weapon falls through the case, you can test it out by placing it in a weapon rack or plaque to see how it behaves, if it is bugged just reload your save and do not put that weapon in the case. If you get the odd unique weapon that also refuses to sit in the weapon rack or on a plaque, and you want to put it on display, just dump it on a table or shelf, probably in one of the old houses unless you built your cellar with display in mind. The junk in the house respawns when the house is left for 10 days, so no point clearing a space to display something.

Things will also pop out of display cases if they do not fit, although sometimes if it almost fits, closing the lid and leaving the house and returning it would have settled.

At this point I have no hopes of Bethesda fixing the problem, I wait for Elder Scrolls 6 and pray to god they do a better job at it next time.

Seriously if this wasnt fixed in the first 2 patches, its never going to get fixed, having to deal with a major issue for a full year is completely unacceptable.