There are a few bugs with the Hearthfire houses, but the chests, safes, endtables, strongboxes, stachels, and wardrobes are all safe storage for certain and I have not heard of any bugs with things disappearing in them. The outside chest is definitely safe.
I did recently encounter a bug where I had my character go into Lakeview Manor, change into her house clothes but kept her armor on her, as i normally do, saved the game and when I reloaded, her bracers, boots, shield and helmet were all missing. It took a few days before I found them--in the safe in the back room of the Main Hall that I use to store valuable amulets. I have no idea why my game put them there but at least the game hadn't completely lost them!
Things that come with the furniture, like alchemy ingredients and food DO respawn in the house (or they are suppose to--they don't always in mine). The apiary, chicken nest and the hawk's nest (on the roof) are suppose to respawn, but I don't think they ever have for my games.
There is a few problems with the display cases. One is people have said that when they re-enter the house, whatever they put in the display case is on the floor. Another more concerning issue reported is people putting things into the display case, it dropping through the case and then through the floor as well, making it irretrievable. Be aware of that one.
There has been reports of things going missing from the weapons racks, namely the metal ones in the entrance hall. What I suspect this is, is weapons fall off the rack and through the floor, making them irretrievable--a known glitch with these types of weapon racks. I have not heard of any issues with the wooden plaque racks in the Main hall. I've never had a weapon go missing from a Hearthfire rack, but I do avoid putting unique items on the entrance hall racks, personally.
Bookshelves in Hearthfire houses appear to be safe, but I do recall one person saying when he/she re-entered their house, all the books in teh library wing had fallen off their shelves and were on the floor. I have yet to encounter this issue myself.
The mannequins appear safe, but prone to the usual Skyrim mannequin glitches, like moving off their pedestals and duplicating armor. My battlemage's upstairs mannequin dupes ebony armor and boots--whatever else she puts on there stays there but the mannequin de-equips them when it dupes a new set of ebony armor and boots. When you activate the mannequin, everything will still be in its inventory. There's a couple things one can try to unglitch this glitch but I've never bothered. As long as things aren't disappearing for good, I'm OK.